https://infovis-wiki.net/w/api.php?action=feedcontributions&feedformat=atom&user=UE-InfoVis0910+0827462 2026-04-21T00:36:49Z User contributions MediaWiki 1.45.3 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23832 2010-01-04T20:14:43Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Area of application===<br /> ------------------------------<br /> <br /> ===Data set analysis===<br /> ------------------------------<br /> <br /> Visualization will display information about family relationships, difference between blood and by marriage relatives, dates of birth and death, length of life, content (happiness) during life, important events in life. From this the overall view should be focused on family relationships and type of family membership. The rest (length of life, birth and death dates, content, important events) are particular details of one person and therefor are not concern of other members in visualization.<br /> <br /> ====Family Relationship====<br /> This information has hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children.<br /> <br /> Data are nominal and discrete. To be able to display the tree we need actually only names and surnames of particular members and then to connect and display them in tree structure. <br /> <br /> ====Difference between blood and by marriage relatives====<br /> This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.<br /> <br /> Value is logical true/false value assigned to relationship between two people.<br /> <br /> ====Length of life====<br /> Since this information is private for person and it won't be displayed as a summary for all members in one graph, it is simple 1-dimensional data structure.<br /> <br /> The value describing length of life is discrete and numerical, e.g. 40 years.<br /> <br /> ====Date of birth and day of death====<br /> As well as length of life is this information also simple 1-dimensional data structure.<br /> Data are discrete and ordinal, e.g. 20. January 1990.<br /> <br /> ====Content (happiness)====<br /> Content of person in particular parts of life is temporal structure.<br /> <br /> The content is ordinal discrete value from following possibilities (ordered from best to worse):<br /> * very high<br /> * high<br /> * middle<br /> * low<br /> * very low<br /> Time is defined in intervals to which person has one of introduced content levels assigned.<br /> <br /> ====Important events in life====<br /> The last information is also temporal structure.<br /> <br /> In comparison to &quot;content&quot;, the &quot;important events in life&quot; is nominal discrete value. Particular values could be &quot;graduation&quot;, &quot;Nobel price for peace&quot;, &quot;imprisoned&quot;, etc. Events are assigned to intervals or instants, i.e. &quot;graduation&quot; can be assigned to instant 20. May 1990, but &quot;imprisoned&quot; will be assigned to interval 20. May 1990 - 20. May 1995.<br /> <br /> ===Target audience===<br /> ------------------------------<br /> Despite the fact that The Simpsons is cartoon, its audience consists mainly of adults. According to &quot;The Simpsons, Innovation and Tradition in a Postmodern TV Family&quot;[Matia Miani] 94 percent of audience was over 18 already in first season. However, our visualization should be targeted on the younger part of this group, in our opinion targeted audience should consist of students with age starting from 17 years. Such set age should guarantee that also students finishing high school will be in targeted audience.<br /> <br /> The targeted audience is not specialized group of people like doctors or electrical engineer and even when they should be students, they will have mostly general education. Thus information should be presented in a simple way with simple and well known words and phrases. Some parts like a gender of person could be displayed for example using icons.<br /> <br /> ===Purpose of visualization===<br /> ------------------------------<br /> Students with age around 18 years should be facing problem whether to continue studies on university or finish with studies. Visualization we are creating can thus help these students to see impact of this decision on the future life. Bart's and Lisa's family tree with important events and happiness during each member's life can be a funny way how this information could be presented. Since Bart and Lisa don't have families, actually they are only kids at the moment, the data presented with introduced members could be taken from real life statistics.<br /> <br /> ===Mockup===<br /> <br /> ====Overview====<br /> [[Image:overview.png]]<br /> <br /> ====Detail of a Subtree and Member====<br /> With mouseover you can get through subtrees. When you click on a member a detail of a member will popup. <br /> <br /> [[Image:subtree-detail.png]]<br /> <br /> ====Subtree Selection for Comparison====<br /> With Ctrl + click you can select subtrees for comparison in both family trees.<br /> <br /> [[Image:compare-detail.png]]<br /> <br /> ====Member Detail====<br /> Contains the name of the member and details about birth, death and length of life. Besides this information you can find here also important events and information about happiness in his/her life.<br /> <br /> The simple data are written out right to their labels.<br /> <br /> Happiness is displayed with slider and timeline that is colored according to happiness in particular lifetime. Slider itself displays color it is pointing at and smiley icon to easier understand the color differentiation.<br /> <br /> Important events are presented with another slider and timeline. Above timeline you can see events where instants have light brown and intervals grey color. This approach provides user with overview of density of events in particular lifetime what helps user to move with slider on the place he/her is interested in. The detail of currently pointed lifetime is displayed under the slider as a list of events.<br /> <br /> [[Image:member-detail.png]]<br /> <br /> ==References==<br /> [Matia Miani] Matia Miani. The Simpsons, Innovation and Tradition in a Postmodern TV Family, Retrieved at: January 2, 2009. http://www.baskerville.it/premiob/2004/Miani.pdf<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Compare-detail.png&diff=23831 2010-01-04T20:10:37Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Subtree-detail.png&diff=23830 2010-01-04T20:09:29Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Overview.png&diff=23829 2010-01-04T20:08:57Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23828 2010-01-04T20:07:18Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Area of application===<br /> ------------------------------<br /> <br /> ===Data set analysis===<br /> ------------------------------<br /> <br /> Visualization will display information about family relationships, difference between blood and by marriage relatives, dates of birth and death, length of life, content (happiness) during life, important events in life. From this the overall view should be focused on family relationships and type of family membership. The rest (length of life, birth and death dates, content, important events) are particular details of one person and therefor are not concern of other members in visualization.<br /> <br /> ====Family Relationship====<br /> This information has hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children.<br /> <br /> Data are nominal and discrete. To be able to display the tree we need actually only names and surnames of particular members and then to connect and display them in tree structure. <br /> <br /> ====Difference between blood and by marriage relatives====<br /> This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.<br /> <br /> Value is logical true/false value assigned to relationship between two people.<br /> <br /> ====Length of life====<br /> Since this information is private for person and it won't be displayed as a summary for all members in one graph, it is simple 1-dimensional data structure.<br /> <br /> The value describing length of life is discrete and numerical, e.g. 40 years.<br /> <br /> ====Date of birth and day of death====<br /> As well as length of life is this information also simple 1-dimensional data structure.<br /> Data are discrete and ordinal, e.g. 20. January 1990.<br /> <br /> ====Content (happiness)====<br /> Content of person in particular parts of life is temporal structure.<br /> <br /> The content is ordinal discrete value from following possibilities (ordered from best to worse):<br /> * very high<br /> * high<br /> * middle<br /> * low<br /> * very low<br /> Time is defined in intervals to which person has one of introduced content levels assigned.<br /> <br /> ====Important events in life====<br /> The last information is also temporal structure.<br /> <br /> In comparison to &quot;content&quot;, the &quot;important events in life&quot; is nominal discrete value. Particular values could be &quot;graduation&quot;, &quot;Nobel price for peace&quot;, &quot;imprisoned&quot;, etc. Events are assigned to intervals or instants, i.e. &quot;graduation&quot; can be assigned to instant 20. May 1990, but &quot;imprisoned&quot; will be assigned to interval 20. May 1990 - 20. May 1995.<br /> <br /> ===Target audience===<br /> ------------------------------<br /> Despite the fact that The Simpsons is cartoon, its audience consists mainly of adults. According to &quot;The Simpsons, Innovation and Tradition in a Postmodern TV Family&quot;[Matia Miani] 94 percent of audience was over 18 already in first season. However, our visualization should be targeted on the younger part of this group, in our opinion targeted audience should consist of students with age starting from 17 years. Such set age should guarantee that also students finishing high school will be in targeted audience.<br /> <br /> The targeted audience is not specialized group of people like doctors or electrical engineer and even when they should be students, they will have mostly general education. Thus information should be presented in a simple way with simple and well known words and phrases. Some parts like a gender of person could be displayed for example using icons.<br /> <br /> ===Purpose of visualization===<br /> ------------------------------<br /> Students with age around 18 years should be facing problem whether to continue studies on university or finish with studies. Visualization we are creating can thus help these students to see impact of this decision on the future life. Bart's and Lisa's family tree with important events and happiness during each member's life can be a funny way how this information could be presented. Since Bart and Lisa don't have families, actually they are only kids at the moment, the data presented with introduced members could be taken from real life statistics.<br /> <br /> ===Mockup===<br /> <br /> ====Overview====<br /> [[Image:overview.png]]<br /> <br /> ====Detail of a Subtree and Member====<br /> [[Image:subtree-detail.png]]<br /> <br /> ====Subtree Selection for Comparison====<br /> [[Image:compare-detail.png]]<br /> <br /> ====Member Detail====<br /> Contains the name of the member and details about birth, death and length of life. Besides this information you can find here also important events and information about happiness in his/her life.<br /> <br /> The simple data are written out right to their labels.<br /> <br /> Happiness is displayed with slider and timeline that is colored according to happiness in particular lifetime. Slider itself displays color it is pointing at and smiley icon to easier understand the color differentiation.<br /> <br /> Important events are presented with another slider and timeline. Above timeline you can see events where instants have light brown and intervals grey color. This approach provides user with overview of density of events in particular lifetime what helps user to move with slider on the place he/her is interested in. The detail of currently pointed lifetime is displayed under the slider as a list of events.<br /> <br /> [[Image:member-detail.png]]<br /> <br /> ==References==<br /> [Matia Miani] Matia Miani. The Simpsons, Innovation and Tradition in a Postmodern TV Family, Retrieved at: January 2, 2009. http://www.baskerville.it/premiob/2004/Miani.pdf<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Member-detail.png&diff=23820 2010-01-03T14:55:23Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23819 2010-01-03T14:54:41Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Area of application===<br /> ------------------------------<br /> <br /> ===Data set analysis===<br /> ------------------------------<br /> <br /> Visualization will display information about family relationships, difference between blood and by marriage relatives, dates of birth and death, length of life, content (happiness) during life, important events in life. From this the overall view should be focused on family relationships and type of family membership. The rest (length of life, birth and death dates, content, important events) are particular details of one person and therefor are not concern of other members in visualization.<br /> <br /> ====Family Relationship====<br /> This information has hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children.<br /> <br /> Data are nominal and discrete. To be able to display the tree we need actually only names and surnames of particular members and then to connect and display them in tree structure. <br /> <br /> ====Difference between blood and by marriage relatives====<br /> This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.<br /> <br /> Value is logical true/false value assigned to relationship between two people.<br /> <br /> ====Length of life====<br /> Since this information is private for person and it won't be displayed as a summary for all members in one graph, it is simple 1-dimensional data structure.<br /> <br /> The value describing length of life is discrete and numerical, e.g. 40 years.<br /> <br /> ====Date of birth and day of death====<br /> As well as length of life is this information also simple 1-dimensional data structure.<br /> Data are discrete and ordinal, e.g. 20. January 1990.<br /> <br /> ====Content (happiness)====<br /> Content of person in particular parts of life is temporal structure.<br /> <br /> The content is ordinal discrete value from following possibilities (ordered from best to worse):<br /> * very high<br /> * high<br /> * middle<br /> * low<br /> * very low<br /> Time is defined in intervals to which person has one of introduced content levels assigned.<br /> <br /> ====Important events in life====<br /> The last information is also temporal structure.<br /> <br /> In comparison to &quot;content&quot;, the &quot;important events in life&quot; is nominal discrete value. Particular values could be &quot;graduation&quot;, &quot;Nobel price for peace&quot;, &quot;imprisoned&quot;, etc. Events are assigned to intervals or instants, i.e. &quot;graduation&quot; can be assigned to instant 20. May 1990, but &quot;imprisoned&quot; will be assigned to interval 20. May 1990 - 20. May 1995.<br /> <br /> ===Target audience===<br /> ------------------------------<br /> Despite the fact that The Simpsons is cartoon, its audience consists mainly of adults. According to &quot;The Simpsons, Innovation and Tradition in a Postmodern TV Family&quot;[Matia Miani] 94 percent of audience was over 18 already in first season. However, our visualization should be targeted on the younger part of this group, in our opinion targeted audience should consist of students with age starting from 17 years. Such set age should guarantee that also students finishing high school will be in targeted audience.<br /> <br /> The targeted audience is not specialized group of people like doctors or electrical engineer and even when they should be students, they will have mostly general education. Thus information should be presented in a simple way with simple and well known words and phrases. Some parts like a gender of person could be displayed for example using icons.<br /> <br /> ===Purpose of visualization===<br /> ------------------------------<br /> Students with age around 18 years should be facing problem whether to continue studies on university or finish with studies. Visualization we are creating can thus help these students to see impact of this decision on the future life. Bart's and Lisa's family tree with important events and happiness during each member's life can be a funny way how this information could be presented. Since Bart and Lisa don't have families, actually they are only kids at the moment, the data presented with introduced members could be taken from real life statistics.<br /> <br /> ===Mockup===<br /> ====Member Detail====<br /> Contains the name of the member and details about birth, death and length of life. Besides this information you can find here also important events and information about happiness in his/her life.<br /> <br /> The simple data are written out right to their labels.<br /> <br /> Happiness is displayed with slider and timeline that is colored according to happiness in particular lifetime. Slider itself displays color it is pointing at and smiley icon to easier understand the color differentiation.<br /> <br /> Important events are presented with another slider and timeline. Above timeline you can see events where instants have light brown and intervals grey color. This approach provides user with overview of density of events in particular lifetime what helps user to move with slider on the place he/her is interested in. The detail of currently pointed lifetime is displayed under the slider as a list of events.<br /> <br /> [[Image:member-detail.png]]<br /> <br /> ==References==<br /> [Matia Miani] Matia Miani. The Simpsons, Innovation and Tradition in a Postmodern TV Family, Retrieved at: January 2, 2009. http://www.baskerville.it/premiob/2004/Miani.pdf<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23817 2010-01-02T15:52:44Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Area of application===<br /> ------------------------------<br /> <br /> ===Data set analysis===<br /> ------------------------------<br /> <br /> Visualization will display information about family relationships, difference between blood and by marriage relatives, dates of birth and death, length of life, content (happiness) during life, important events in life. From this the overall view should be focused on family relationships and type of family membership. The rest (length of life, birth and death dates, content, important events) are particular details of one person and therefor are not concern of other members in visualization.<br /> <br /> ====Family Relationship====<br /> This information has hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children.<br /> <br /> Data are nominal and discrete. To be able to display the tree we need actually only names and surnames of particular members and then to connect and display them in tree structure. <br /> <br /> ====Difference between blood and by marriage relatives====<br /> This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.<br /> <br /> Value is logical true/false value assigned to relationship between two people.<br /> <br /> ====Length of life====<br /> Since this information is private for person and it won't be displayed as a summary for all members in one graph, it is simple 1-dimensional data structure.<br /> <br /> The value describing length of life is discrete and numerical, e.g. 40 years.<br /> <br /> ====Date of birth and day of death====<br /> As well as length of life is this information also simple 1-dimensional data structure.<br /> Data are discrete and ordinal, e.g. 20. January 1990.<br /> <br /> ====Content (happiness)====<br /> Content of person in particular parts of life is temporal structure.<br /> <br /> The content is ordinal discrete value from following possibilities (ordered from best to worse):<br /> * very high<br /> * high<br /> * middle<br /> * low<br /> * very low<br /> Time is defined in intervals to which person has one of introduced content levels assigned.<br /> <br /> ====Important events in life====<br /> The last information is also temporal structure.<br /> <br /> In comparison to &quot;content&quot;, the &quot;important events in life&quot; is nominal discrete value. Particular values could be &quot;graduation&quot;, &quot;Nobel price for peace&quot;, &quot;imprisoned&quot;, etc. Events are assigned to intervals or instants, i.e. &quot;graduation&quot; can be assigned to instant 20. May 1990, but &quot;imprisoned&quot; will be assigned to interval 20. May 1990 - 20. May 1995.<br /> <br /> ===Target audience===<br /> ------------------------------<br /> Despite the fact that The Simpsons is cartoon, its audience consists mainly of adults. According to &quot;The Simpsons, Innovation and Tradition in a Postmodern TV Family&quot;[Matia Miani] 94 percent of audience was over 18 already in first season. However, our visualization should be targeted on the younger part of this group, in our opinion targeted audience should consist of students with age starting from 17 years. Such set age should guarantee that also students finishing high school will be in targeted audience.<br /> <br /> The targeted audience is not specialized group of people like doctors or electrical engineer and even when they should be students, they will have mostly general education. Thus information should be presented in a simple way with simple and well known words and phrases. Some parts like a gender of person could be displayed for example using icons.<br /> <br /> ===Purpose of visualization===<br /> ------------------------------<br /> Students with age around 18 years should be facing problem whether to continue studies on university or finish with studies. Visualization we are creating can thus help these students to see impact of this decision on the future life. Bart's and Lisa's family tree with important events and happiness during each member's life can be a funny way how this information could be presented. Since Bart and Lisa don't have families, actually they are only kids at the moment, the data presented with introduced members could be taken from real life statistics.<br /> <br /> <br /> ==References==<br /> [Matia Miani] Matia Miani. The Simpsons, Innovation and Tradition in a Postmodern TV Family, Retrieved at: January 2, 2009. http://www.baskerville.it/premiob/2004/Miani.pdf<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23815 2010-01-02T15:36:04Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Area of application===<br /> ------------------------------<br /> <br /> ===Data set analysis===<br /> ------------------------------<br /> <br /> Visualization will display information about family relationships, difference between blood and by marriage relatives, dates of birth and death, length of life, content (happiness) during life, important events in life. From this the overall view should be focused on family relationships and type of family membership. The rest (length of life, birth and death dates, content, important events) are particular details of one person and therefor are not concern of other members in visualization.<br /> <br /> ====Family Relationship====<br /> This information has hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children.<br /> <br /> Data are nominal and discrete. To be able to display the tree we need actually only names and surnames of particular members and then to connect and display them in tree structure. <br /> <br /> ====Difference between blood and by marriage relatives====<br /> This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.<br /> <br /> Value is logical true/false value assigned to relationship between two people.<br /> <br /> ====Length of life====<br /> Since this information is private for person and it won't be displayed as a summary for all members in one graph, it is simple 1-dimensional data structure.<br /> <br /> The value describing length of life is discrete and numerical, e.g. 40 years.<br /> <br /> ====Date of birth and day of death====<br /> As well as length of life is this information also simple 1-dimensional data structure.<br /> Data are discrete and ordinal, e.g. 20. January 1990.<br /> <br /> ====Content (happiness)====<br /> Content of person in particular parts of life is temporal structure.<br /> <br /> The content is ordinal discrete value from following possibilities (ordered from best to worse):<br /> * very high<br /> * high<br /> * middle<br /> * low<br /> * very low<br /> Time is defined in intervals to which person has one of introduced content levels assigned.<br /> <br /> ====Important events in life====<br /> The last information is also temporal structure.<br /> <br /> In comparison to &quot;content&quot;, the &quot;important events in life&quot; is nominal discrete value. Particular values could be &quot;graduation&quot;, &quot;Nobel price for peace&quot;, &quot;imprisoned&quot;, etc. Events are assigned to intervals or instants, i.e. &quot;graduation&quot; can be assigned to instant 20. May 1990, but &quot;imprisoned&quot; will be assigned to interval 20. May 1990 - 20. May 1995.<br /> <br /> ===Target audience===<br /> ------------------------------<br /> Despite the fact that The Simpsons is cartoon, its audience consists mainly of adults. According to &quot;The Simpsons, Innovation and Tradition in a Postmodern TV Family&quot;[Matia Miani] 94 percent of audience was over 18 already in first season. However, our visualization should be targeted on the younger part of this group, in our opinion targeted audience should consist of students with age starting from 17 years. Such set age should guarantee that also students finishing high school will be in targeted audience.<br /> The information should be presented in a simple way with simple and well known words and phrases. The targeted audience is not specialized group of people like doctors or electrical engineer and does not have to be necessarily well educated.<br /> <br /> ===Purpose of visualization===<br /> ------------------------------<br /> Students with age around 18 years should be facing problem whether to continue studies on university or finish with studies. Visualization we are creating can thus help these students to see impact of this decision on the future life. Bart's and Lisa's family tree with important events and happiness during each member's life can be a funny way how this information could be presented. Since Bart and Lisa don't have families, actually they are only kids at the moment, the data presented with introduced members could be taken from real life statistics.<br /> <br /> <br /> ==References==<br /> [Matia Miani] Matia Miani. The Simpsons, Innovation and Tradition in a Postmodern TV Family, Retrieved at: January 2, 2009. http://www.baskerville.it/premiob/2004/Miani.pdf<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23814 2010-01-02T15:13:59Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Area of application===<br /> ------------------------------<br /> <br /> ===Data set analysis===<br /> ------------------------------<br /> <br /> Visualization will display information about family relationships, difference between blood and by marriage relatives, dates of birth and death, length of life, content (happiness) during life, important events in life. From this the overall view should be focused on family relationships and type of family membership. The rest (length of life, birth and death dates, content, important events) are particular details of one person and therefor are not concern of other members in visualization.<br /> <br /> ====Family Relationship====<br /> This information has hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children.<br /> <br /> Data are nominal and discrete. To be able to display the tree we need actually only names and surnames of particular members and then to connect and display them in tree structure. <br /> <br /> ====Difference between blood and by marriage relatives====<br /> This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.<br /> <br /> Value is logical true/false value assigned to relationship between two people.<br /> <br /> ====Length of life====<br /> Since this information is private for person and it won't be displayed as a summary for all members in one graph, it is simple 1-dimensional data structure.<br /> <br /> The value describing length of life is discrete and numerical, e.g. 40 years.<br /> <br /> ====Date of birth and day of death====<br /> As well as length of life is this information also simple 1-dimensional data structure.<br /> Data are discrete and ordinal, e.g. 20. January 1990.<br /> <br /> ====Content (happiness)====<br /> Content of person in particular parts of life is temporal structure.<br /> <br /> The content is ordinal discrete value from following possibilities (ordered from best to worse):<br /> * very high<br /> * high<br /> * middle<br /> * low<br /> * very low<br /> Time is defined in intervals to which person has one of introduced content levels assigned.<br /> <br /> ====Important events in life====<br /> The last information is also temporal structure.<br /> <br /> In comparison to &quot;content&quot;, the &quot;important events in life&quot; is nominal discrete value. Particular values could be &quot;graduation&quot;, &quot;Nobel price for peace&quot;, &quot;imprisoned&quot;, etc. Events are assigned to intervals or instants, i.e. &quot;graduation&quot; can be assigned to instant 20. May 1990, but &quot;imprisoned&quot; will be assigned to interval 20. May 1990 - 20. May 1995.<br /> <br /> ===Target audience===<br /> ------------------------------<br /> Despite the fact that The Simpsons is cartoon, its audience consists mainly of adults. According to &quot;The Simpsons, Innovation and Tradition in a Postmodern TV Family&quot;[Matia Miani] 94 percent of audience was over 18 already in first season. However, our visualization should be targeted on the younger part of this group, in our opinion targeted audience should consist of students with age starting from 17 years. Such set age should guarantee that also students finishing high school will be in targeted audience. These students are before decision whether to go to university or finish with studying and start to work and presented Bart's and Lisa's family tree with important events and happiness during each member's life can be a funny way how to show that the right decision is important.<br /> <br /> ===Purpose of visualization===<br /> ------------------------------<br /> <br /> ==References==<br /> [Matia Miani] Matia Miani. The Simpsons, Innovation and Tradition in a Postmodern TV Family, Retrieved at: January 2, 2009. http://www.baskerville.it/premiob/2004/Miani.pdf<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23813 2010-01-02T14:54:07Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Area of application===<br /> ------------------------------<br /> <br /> ===Data set analysis===<br /> ------------------------------<br /> <br /> Visualization will display information about family relationships, difference between blood and by marriage relatives, dates of birth and death, length of life, content (happiness) during life, important events in life. From this the overall view should be focused on family relationships and type of family membership. The rest (length of life, birth and death dates, content, important events) are particular details of one person and therefor are not concern of other members in visualization.<br /> <br /> ====Family Relationship====<br /> This information has hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children.<br /> <br /> Data are nominal and discrete. To be able to display the tree we need actually only names and surnames of particular members and then to connect and display them in tree structure. <br /> <br /> ====Difference between blood and by marriage relatives====<br /> This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.<br /> <br /> Value is logical true/false value assigned to relationship between two people.<br /> <br /> ====Length of life====<br /> Since this information is private for person and it won't be displayed as a summary for all members in one graph, it is simple 1-dimensional data structure.<br /> <br /> The value describing length of life is discrete and numerical, e.g. 40 years.<br /> <br /> ====Date of birth and day of death====<br /> As well as length of life is this information also simple 1-dimensional data structure.<br /> Data are discrete and ordinal, e.g. 20. January 1990.<br /> <br /> ====Content (happiness)====<br /> Content of person in particular parts of life is temporal structure.<br /> <br /> The content is ordinal discrete value from following possibilities (ordered from best to worse):<br /> * very high<br /> * high<br /> * middle<br /> * low<br /> * very low<br /> Time is defined in intervals to which person has one of introduced content levels assigned.<br /> <br /> ====Important events in life====<br /> The last information is also temporal structure.<br /> <br /> In comparison to &quot;content&quot;, the &quot;important events in life&quot; is nominal discrete value. Particular values could be &quot;graduation&quot;, &quot;Nobel price for peace&quot;, &quot;imprisoned&quot;, etc. Events are assigned to intervals or instants, i.e. &quot;graduation&quot; can be assigned to instant 20. May 1990, but &quot;imprisoned&quot; will be assigned to interval 20. May 1990 - 20. May 1995.<br /> <br /> ===Target audience===<br /> ------------------------------<br /> Despite the fact that The Simpsons is cartoon, its audience consists mainly of adults. According to &quot;The Simpsons, Innovation and Tradition in a Postmodern TV Family&quot;[Matia Miani] 94 percent of audience was over 18 already in first season. However, our visualization should be targeted on the younger part of this group. <br /> <br /> ===Purpose of visualization===<br /> ------------------------------<br /> <br /> ==References==<br /> [Matia Miani] Matia Miani. The Simpsons, Innovation and Tradition in a Postmodern TV Family, Retrieved at: January 2, 2009. http://www.baskerville.it/premiob/2004/Miani.pdf<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23812 2010-01-02T12:30:41Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Data set analysis===<br /> ------------------------------<br /> <br /> Visualization will display information about family relationships, difference between blood and by marriage relatives, dates of birth and death, length of life, content (happiness) during life, important events in life. From this the overall view should be focused on family relationships and type of family membership. The rest (length of life, birth and death dates, content, important events) are particular details of one person and therefor are not concern of other members in visualization.<br /> <br /> ====Family Relationship====<br /> This information has hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children.<br /> <br /> Data are nominal and discrete. To be able to display the tree we need actually only names and surnames of particular members and then to connect and display them in tree structure. <br /> <br /> ====Difference between blood and by marriage relatives====<br /> This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.<br /> <br /> Value is logical true/false value assigned to relationship between two people.<br /> <br /> ====Length of life====<br /> Since this information is private for person and it won't be displayed as a summary for all members in one graph, it is simple 1-dimensional data structure.<br /> <br /> The value describing length of life is discrete and numerical, e.g. 40 years.<br /> <br /> ====Date of birth and day of death====<br /> As well as length of life is this information also simple 1-dimensional data structure.<br /> Data are discrete and ordinal, e.g. 20. January 1990.<br /> <br /> ====Content (happiness)====<br /> Content of person in particular parts of life is temporal structure.<br /> <br /> The content is ordinal discrete value from following possibilities (ordered from best to worse):<br /> * very high<br /> * high<br /> * middle<br /> * low<br /> * very low<br /> Time is defined in intervals to which person has one of introduced content levels assigned.<br /> <br /> ====Important events in life====<br /> The last information is also temporal structure.<br /> <br /> In comparison to &quot;content&quot;, the &quot;important events in life&quot; is nominal discrete value. Particular values could be &quot;graduation&quot;, &quot;Nobel price for peace&quot;, &quot;imprisoned&quot;, etc. Events are assigned to intervals or instants, i.e. &quot;graduation&quot; can be assigned to instant 20. May 1990, but &quot;imprisoned&quot; will be assigned to interval 20. May 1990 - 20. May 1995.<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23811 2010-01-02T12:29:21Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Data set analysis===<br /> ------------------------------<br /> <br /> Visualization will display information about family relationships, difference between blood and by marriage relatives, dates of birth and death, length of life, content (happiness) during life, important events in life. From this the overall view should be focused on family relationships and type of family membership. The rest (length of life, birth and death dates, content, important events) are particular details of one person and therefor are not concern of other members in visualization.<br /> <br /> ====Family Relationship====<br /> This information has hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children.<br /> <br /> Data are nominal and discrete. To be able to display the tree we need actually only names and surnames of particular members and then to connect and display them in tree structure. <br /> <br /> <br /> ====Difference between blood and by marriage relatives====<br /> This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.<br /> <br /> Value is logical true/false value assigned to relationship between two people.<br /> <br /> <br /> ====Length of life====<br /> Since this information is private for person and it won't be displayed as a summary for all members in one graph, it is simple 1-dimensional data structure.<br /> <br /> The value describing length of life is discrete and numerical, e.g. 40 years.<br /> <br /> <br /> ====Date of birth and day of death====<br /> As well as length of life is this information also simple 1-dimensional data structure.<br /> Data are discrete and ordinal, e.g. 20. January 1990.<br /> <br /> <br /> ====Content (happiness)====<br /> Content of person in particular parts of life is temporal structure.<br /> <br /> The content is ordinal discrete value from following possibilities (ordered from best to worse):<br /> * very high<br /> * high<br /> * middle<br /> * low<br /> * very low<br /> Time is defined in intervals to which person has one of introduced content levels assigned.<br /> <br /> <br /> ====Important events in life====<br /> The last information is also temporal structure.<br /> <br /> In comparison to &quot;content&quot;, the &quot;important events in life&quot; is nominal discrete value. Particular values could be &quot;graduation&quot;, &quot;Nobel price for peace&quot;, &quot;imprisoned&quot;, etc. Events are assigned to intervals or instants, i.e. &quot;graduation&quot; can be assigned to instant 20. May 1990, but &quot;imprisoned&quot; will be assigned to interval 20. May 1990 - 20. May 1995.<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23791 2009-12-29T14:54:09Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Data set description===<br /> ------------------------------<br /> <br /> <br /> family relationship:<br /> * hierarchical structure where the root of each tree are the oldest ancestors (Lisa and her husband, Bart and his wife) and leaf nodes are their (grand...)children<br /> <br /> <br /> difference between blood relative and by marriage relative:<br /> * logical true/false value assigned to relationship between two people<br /> <br /> <br /> life length:<br /> * discrete numerical data<br /> <br /> <br /> date of birth and day of death:<br /> * discrete ordinal data<br /> <br /> <br /> content (happiness):<br /> * 2-dimensional data structure<br /> * ordinal discrete values descibe content<br /> * continuous values descibe time in life to which the content is assigned<br /> <br /> <br /> important events in life:<br /> * 2-dimensional structure<br /> * nominal discrete data values to describe events during life<br /> * intervals or discrete numerical values to define lifetime connected to event<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_4&diff=23790 2009-12-29T14:46:51Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]<br /> === Zu erstellende Visualisierung ===<br /> -------------------------------<br /> * Stammbaum der Nachkommen von Lisa und Bart Simpson*<br /> <br /> ...Visualisierung der Nachkommen von Lisa Simpson sowie der Nachkommen von Bart Simpson. Dabei sollen zwei Stammbäume entstehen - einer von Bart und einer von Lisa - die dann miteinander verglichen werden können. Zuerst kommen Lisa und Bart, dann deren Kinder, ihre Enkel, etc. (mind 4 Generationen). Da es noch keine Nachkommen gibt, können diese frei erfunden werden.<br /> <br /> Die Visualisierung soll folgende Informationen darstellen:<br /> <br /> - Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),<br /> <br /> - Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,<br /> <br /> - Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,<br /> <br /> - wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)<br /> <br /> - Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.<br /> <br /> Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.<br /> Verpflichtend:<br /> Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.<br /> + mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)<br /> <br /> Allgemein:<br /> <br /> - Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).<br /> <br /> - Die bisher erlernten Design-Prinzipien sollen umgesetzt werden z.B.: Optimierung der Data-ink ratio (keine Comics!), visuelle Attribute (Größe, Farbe, Position, etc.) sollen sinnvoll eingesetzt werden (Information darstellen).<br /> <br /> - Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.<br /> <br /> - Alle nicht angeführten Daten können frei erfunden werden.<br /> ===Data set description===<br /> ------------------------------<br /> <br /> <br /> family relationship:<br /> * 2-dimensional data structure, 1. axis contains parents and 2. axis contains children<br /> <br /> <br /> difference between blood relative and by marriage relative:<br /> * logical true/false value assigned to relationship between two people<br /> <br /> <br /> life length:<br /> * discrete numerical data<br /> <br /> <br /> date of birth and day of death:<br /> * discrete ordinal data<br /> <br /> <br /> content (happiness):<br /> * 2-dimensional data structure<br /> * ordinal discrete values descibe content<br /> * continuous values descibe time in life to which the content is assigned<br /> <br /> <br /> important events in life:<br /> * 2-dimensional structure<br /> * nominal discrete data values to describe events during life<br /> * intervals or discrete numerical values to define lifetime connected to event<br /> <br /> ------------------------------<br /> <br /> == Links ==<br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_3&diff=23658 2009-12-08T13:45:11Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe3.html Beschreibung der Aufgabe 3]<br /> === Zu verbessernde Grafik ===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> [[Image:nyt.gif]]<br /> <br /> <br /> == Ausarbeitung ==<br /> <br /> ===Critics===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> * If you are not familiar with those kinds of diagrams, they are a little hard to read at a first glance. It took me a few minutes until I understood, that &quot;Total&quot; is a company. Therefore the graphic made no sense at first. Of course, if you have the graphics embedded in an article this confusion would not happen at all. But still, if you have to study a graphics in a news paper (and not a scientific paper) for one or two minutes, just to understand it, you may just skip it. So in the context of a simple news paper this diagram may be a little to complicated.<br /> <br /> * The y-axes shows the growth rate of the companies. This is quite easy to understand. What could be a little irritating are the circles that represent the total production of the year. At a first glance it looks like the circles are related to values of the y-axes, but they are absolutely not (only the center of the circle is relevant). The size of the circle represents information which is absolutely independent from the y-axes.<br /> <br /> * Graph takes too much place because of the size of bubbles and the way how they are organized on y-axes. This together with title and description under Total bubble causes, that user misses possibility of quick overview and understanding of the chart.<br /> <br /> * The size of the circles and the growth rate (location on the y-axes and numbered value) alone don't really give you a hint, how the amount of production was in 2002. You can only use the size of the circles to compare this year's production of every company with all other. But wouldn't it also be interesting if you were able to compare the oil production for each company with its own production from 2002? Of course, the growth rate gives you exactly this information, but not in an eye-catching way. It would be, if you had a second circle for each company in the background (with the same center) in another color. Now we would have the size of the circles, that shows you the production amount, the second circle in the back, that gives you an idea how the production amount of each company has changed and the position on the diagram which makes it easy to compare the growth rates of one company with all others. The advantage of this redundant information is the easier way of comparison - the disadvantage is that it maybe makes the diagram even harder to understand at first ('cause there is one more information layer). <br /> <br /> *Beside the fact that the data presented is not easy to understand, it is not clear what information should be focused. The chart shows a comparison of the major oil producers with detailed written information about the situation of Total. This divides the chart logically and visually into two parts, which can confuse the message. In my opinion this chart wants to present relation between the size of production and growth rate. It is nice that Total is emphasized by different color, but it is the size of production what will be user focused on because of the bubble, not growth rate.<br /> <br /> *Further, it may be criticized that the legends describing the circles are positioned on the right hand side and the numbers describing the percentage of growth are on the left. As most readers start to read from left to right, the focus is first on the percentage of growth. Then they go further on to check the names of the companies. But this is the wrong way, because the original question is about the companies and their growth and not about the growth. For this reason the reader lose time to get the information. In addition, the scale produces a lot of white space without information, as between ExxonMobil and Royal Dutch Shell. <br /> <br /> * The units for y-axes are visible only on first and last value and there is no general description of y-axes. User who starts to read chart from the 0 on axes won't know which units are used.<br /> <br /> ===Redesigned Graph===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> &lt;!--[[Image:improved_graph_oil_prod.jpg]]--&gt;<br /> [[Image:improved_graph_oil_prod-2.png]]<br /> <br /> ===Description of improvements===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> *The data which should be focused in the first visual layer is clearly in front, underlined by bigger letters (percentage of growth) and different colours (green bars). The supporting components are designed with different colours and smaller letters to draw not to much attention.<br /> <br /> * In the new version of the chart the scale is completely deleted. Instead numbers on the right side of bars show the growth. Production numbers where moved into bars where they are written in small letters for both calculated years. This allows a much more compact and clear presentation of the data and shows that growth is calculated according to production in years 2002 and 2008.<br /> <br /> *As the sequence was defined by the scale, the companies are already in the right order. It also makes sense to use this order as group definition for the new data bar. The new data bar is now possible because the original circles are now replaced by bars, which are visually easier to compare. <br /> <br /> * Bars for Total company are presented in different color to achieve user's attention. This approach was used also in the original chart, however now we have differed each important part of it's data particularly percentage of growth rate, production bars and the name.<br /> <br /> * Now the chart intuitive communicates a clear message through a better presentation of the data, even less elements are used. For this the Data-Ink Ration improved a lot comparing the new version with the old version.<br /> <br /> * Title and description was moved to the top of the chart where it doesn't hinder in reading the chart.</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_3&diff=23653 2009-12-08T13:08:31Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe3.html Beschreibung der Aufgabe 3]<br /> === Zu verbessernde Grafik ===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> [[Image:nyt.gif]]<br /> <br /> <br /> == Ausarbeitung ==<br /> <br /> ===Critics===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> * If you are not familiar with those kinds of diagrams, they are a little hard to read at a first glance. It took me a few minutes until I understood, that &quot;Total&quot; is a company. Therefore the graphic made no sense at first. Of course, if you have the graphics embedded in an article this confusion would not happen at all. But still, if you have to study a graphics in a news paper (and not a scientific paper) for one or two minutes, just to understand it, you may just skip it. So in the context of a simple news paper this diagram may be a little to complicated.<br /> <br /> * The y-axes shows the growth rate of the companies. This is quite easy to understand. What could be a little irritating are the circles that represent the total production of the year. At a first glance it looks like the circles are related to values of the y-axes, but they are absolutely not (only the center of the circle is relevant). The size of the circle represents information which is absolutely independent from the y-axes.<br /> <br /> * Graph takes too much place because of the size of bubbles and the way how they are organized on y-axes. This together with title and description under Total bubble causes, that user misses possibility of quick overview and understanding of the chart.<br /> <br /> * The size of the circles and the growth rate (location on the y-axes and numbered value) alone don't really give you a hint, how the amount of production was in 2002. You can only use the size of the circles to compare this year's production of every company with all other. But wouldn't it also be interesting if you were able to compare the oil production for each company with its own production from 2002? Of course, the growth rate gives you exactly this information, but not in an eye-catching way. It would be, if you had a second circle for each company in the background (with the same center) in another color. Now we would have the size of the circles, that shows you the production amount, the second circle in the back, that gives you an idea how the production amount of each company has changed and the position on the diagram which makes it easy to compare the growth rates of one company with all others. The advantage of this redundant information is the easier way of comparison - the disadvantage is that it maybe makes the diagram even harder to understand at first ('cause there is one more information layer). <br /> <br /> *Beside the fact that the data presented is not easy to understand, it is not clear what information should be focused. The chart shows a comparison of the major oil producers with detailed written information about the situation of Total. This divides the chart logically and visually into two parts, which can confuse the message. In my opinion this chart wants to present relation between the size of production and growth rate. It is nice that Total is emphasized by different color, but it is the size of production what will be user focused on because of the bubble, not growth rate.<br /> <br /> *Further, it may be criticized that the legends describing the circles are positioned on the right hand side and the numbers describing the percentage of growth are on the left. As most readers start to read from left to right, the focus is first on the percentage of growth. Then they go further on to check the names of the companies. But this is the wrong way, because the original question is about the companies and their growth and not about the growth. For this reason the reader lose time to get the information. In addition, the scale produces a lot of white space without information, as between ExxonMobil and Royal Dutch Shell. <br /> <br /> ===Redesigned Graph===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> &lt;!--[[Image:improved_graph_oil_prod.jpg]]--&gt;<br /> [[Image:improved_graph_oil_prod-2.png]]<br /> <br /> ===Description of improvements===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> *The data which should be focused in the first visual layer is clearly in front, underlined by bigger letters (percentage of growth) and different colours (green bars). The supporting components are designed with different colours and smaller letters to draw not to much attention.<br /> <br /> * In the new version of the chart the scale is completely deleted. Instead numbers inside the bars show the growth. This allows a much more compact and clear presentation of the data.<br /> <br /> *As the sequence was defined by the scale, the companies are already in the right order. It also makes sense to use this order as group definition for the new data bar. The new data bar is now possible because the original circles are now replaced by bars, which are visually easier to compare. <br /> <br /> * Now the chart intuitive communicates a clear message through a better presentation of the data, even less elements are used. For this the Data-Ink Ration improved a lot comparing the new version with the old version.</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_3&diff=23652 2009-12-08T12:55:30Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe3.html Beschreibung der Aufgabe 3]<br /> === Zu verbessernde Grafik ===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> [[Image:nyt.gif]]<br /> <br /> <br /> == Ausarbeitung ==<br /> <br /> ===Critics===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> * If you are not familiar with those kinds of diagrams, they are a little hard to read at a first glance. It took me a few minutes until I understood, that &quot;Total&quot; is a company. Therefore the graphic made no sense at first. Of course, if you have the graphics embedded in an article this confusion would not happen at all. But still, if you have to study a graphics in a news paper (and not a scientific paper) for one or two minutes, just to understand it, you may just skip it. So in the context of a simple news paper this diagram may be a little to complicated.<br /> <br /> * The y-axes shows the growth rate of the companies. This is quite easy to understand. What could be a little irritating are the circles that represent the total production of the year. At a first glance it looks like the circles are related to values of the y-axes, but they are absolutely not (only the center of the circle is relevant). The size of the circle represents information which is absolutely independent from the y-axes.<br /> <br /> * The size of the circles and the growth rate (location on the y-axes and numbered value) alone don't really give you a hint, how the amount of production was in 2002. You can only use the size of the circles to compare this year's production of every company with all other. But wouldn't it also be interesting if you were able to compare the oil production for each company with its own production from 2002? Of course, the growth rate gives you exactly this information, but not in an eye-catching way. It would be, if you had a second circle for each company in the background (with the same center) in another color. Now we would have the size of the circles, that shows you the production amount, the second circle in the back, that gives you an idea how the production amount of each company has changed and the position on the diagram which makes it easy to compare the growth rates of one company with all others. The advantage of this redundant information is the easier way of comparison - the disadvantage is that it maybe makes the diagram even harder to understand at first ('cause there is one more information layer). <br /> <br /> *Beside the fact that the data presented is not easy to understand, it is not clear what information should be focused. The chart shows a comparison of the major oil producers with detailed written information about the situation of Total. This divides the chart logically and visually into two parts, which can confuse the message. I think in this case the more important information should be an overview of all oil producers, which then can be referenced in a text where the situation of Total is explained in more detail.<br /> <br /> *Further, it may be criticized that the legends describing the circles are positioned on the right hand side and the numbers describing the percentage of growth are on the left. As most readers start to read from left to right, the focus is first on the percentage of growth. Then they go further on to check the names of the companies. But this is the wrong way, because the original question is about the companies and their growth and not about the growth. For this reason the reader lose time to get the information. In addition, the scale produces a lot of white space without information, as between ExxonMobil and Royal Dutch Shell. <br /> <br /> ===Redesigned Graph===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> &lt;!--[[Image:improved_graph_oil_prod.jpg]]--&gt;<br /> [[Image:improved_graph_oil_prod-2.png]]<br /> <br /> ===Description of improvements===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> *The data which should be focused in the first visual layer is clearly in front, underlined by bigger letters (percentage of growth) and different colours (green bars). The supporting components are designed with different colours and smaller letters to draw not to much attention.<br /> <br /> * In the new version of the chart the scale is completely deleted. Instead numbers inside the bars show the growth. This allows a much more compact and clear presentation of the data.<br /> <br /> *As the sequence was defined by the scale, the companies are already in the right order. It also makes sense to use this order as group definition for the new data bar. The new data bar is now possible because the original circles are now replaced by bars, which are visually easier to compare. <br /> <br /> * Now the chart intuitive communicates a clear message through a better presentation of the data, even less elements are used. For this the Data-Ink Ration improved a lot comparing the new version with the old version.</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Improved_graph_oil_prod-2.png&diff=23651 2009-12-08T12:54:49Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_3&diff=23650 2009-12-08T12:54:04Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe3.html Beschreibung der Aufgabe 3]<br /> === Zu verbessernde Grafik ===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> [[Image:nyt.gif]]<br /> <br /> <br /> == Ausarbeitung ==<br /> <br /> ===Critics===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> * If you are not familiar with those kinds of diagrams, they are a little hard to read at a first glance. It took me a few minutes until I understood, that &quot;Total&quot; is a company. Therefore the graphic made no sense at first. Of course, if you have the graphics embedded in an article this confusion would not happen at all. But still, if you have to study a graphics in a news paper (and not a scientific paper) for one or two minutes, just to understand it, you may just skip it. So in the context of a simple news paper this diagram may be a little to complicated.<br /> <br /> * The y-axes shows the growth rate of the companies. This is quite easy to understand. What could be a little irritating are the circles that represent the total production of the year. At a first glance it looks like the circles are related to values of the y-axes, but they are absolutely not (only the center of the circle is relevant). The size of the circle represents information which is absolutely independent from the y-axes.<br /> <br /> * The size of the circles and the growth rate (location on the y-axes and numbered value) alone don't really give you a hint, how the amount of production was in 2002. You can only use the size of the circles to compare this year's production of every company with all other. But wouldn't it also be interesting if you were able to compare the oil production for each company with its own production from 2002? Of course, the growth rate gives you exactly this information, but not in an eye-catching way. It would be, if you had a second circle for each company in the background (with the same center) in another color. Now we would have the size of the circles, that shows you the production amount, the second circle in the back, that gives you an idea how the production amount of each company has changed and the position on the diagram which makes it easy to compare the growth rates of one company with all others. The advantage of this redundant information is the easier way of comparison - the disadvantage is that it maybe makes the diagram even harder to understand at first ('cause there is one more information layer). <br /> <br /> *Beside the fact that the data presented is not easy to understand, it is not clear what information should be focused. The chart shows a comparison of the major oil producers with detailed written information about the situation of Total. This divides the chart logically and visually into two parts, which can confuse the message. I think in this case the more important information should be an overview of all oil producers, which then can be referenced in a text where the situation of Total is explained in more detail.<br /> <br /> *Further, it may be criticized that the legends describing the circles are positioned on the right hand side and the numbers describing the percentage of growth are on the left. As most readers start to read from left to right, the focus is first on the percentage of growth. Then they go further on to check the names of the companies. But this is the wrong way, because the original question is about the companies and their growth and not about the growth. For this reason the reader lose time to get the information. In addition, the scale produces a lot of white space without information, as between ExxonMobil and Royal Dutch Shell. <br /> <br /> ===Redesigned Graph===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> &lt;!--[[Image:improved_graph_oil_prod.jpg]]--&gt;<br /> [[Image:improved_graph_oil_prod-2.jpg]]<br /> ===Description of improvements===<br /> ------------------------------- &lt;br&gt; &lt;br&gt;<br /> <br /> *The data which should be focused in the first visual layer is clearly in front, underlined by bigger letters (percentage of growth) and different colours (green bars). The supporting components are designed with different colours and smaller letters to draw not to much attention.<br /> <br /> * In the new version of the chart the scale is completely deleted. Instead numbers inside the bars show the growth. This allows a much more compact and clear presentation of the data.<br /> <br /> *As the sequence was defined by the scale, the companies are already in the right order. It also makes sense to use this order as group definition for the new data bar. The new data bar is now possible because the original circles are now replaced by bars, which are visually easier to compare. <br /> <br /> * Now the chart intuitive communicates a clear message through a better presentation of the data, even less elements are used. For this the Data-Ink Ration improved a lot comparing the new version with the old version.</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_2&diff=23192 2009-11-12T21:15:25Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]<br /> === Original table ===<br /> [[Image:expenditure-categ.JPG]]<br /> <br /> === Critic on original table ===<br /> <br /> Missing unit in expenditure columns.<br /> <br /> === Redesigned table ===<br /> [[Image:expenditure-categ-repaired-2.png]]<br /> <br /> === Changes applied to table ===<br /> <br /> Second row, the one with ordinal numerals had no meaningful function. Because of that we decided to remove it completely from the table.<br /> <br /> It is a convention that numbers are aligned to the right. When the numbers in column are displayed with the same precision, i.e. two decimal places like in this table, reader can more easily compare numbers one under another because hundreds are under hundreds, thousands under thousands and so on.<br /> <br /> There should be units declared for each column at least in header. However there were no units declared in original table so we cannot say what currency is the amount displayed in. However there was added % sign to each cell in percentage columns. It is a convention too. Reader sees that the number describes percentage without looking into header row.<br /> <br /> We changed also a format of the numbers, to make processing and comparing of numbers easier for reader. Comma was placed to the left of every three whole-number digits to divide thousands from millions, millions from billions, etc. Reader can more easily count digits in the number.<br /> <br /> Another change we made is addition of &quot;Education type&quot; into header row and removing of word &quot;Education&quot; from each row in first column. Thus the cells are shorter and don't have to be wrapped to two or more lines because of redundant information. Each line has now the same height.<br /> <br /> Almost all rules were removed. They remained only on places where they are used to divide header or summary from the rest of data. After removing of rules we got body of table without any guideline in which direction data should be read. Because of that we decided to use light background color for columns. Reader can now easily compare expenditures for each type of education and find the results for each row and each column.<br /> <br /> == Links ==<br /> <br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_2&diff=23191 2009-11-12T20:57:39Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]<br /> === Original table ===<br /> [[Image:expenditure-categ.JPG]]<br /> <br /> === Critic on original table ===<br /> <br /> Missing unit in expenditure columns.<br /> <br /> === Redesigned table ===<br /> [[Image:expenditure-categ-repaired-2.png]]<br /> <br /> === Changes applied to table ===<br /> <br /> Second row, the one with ordinal numerals had no meaningful function. Because of that we decided to remove it completely from the table.<br /> <br /> It is a convention that numbers are aligned to the right. When the numbers in column are displayed with the same precision, i.e. two decimal places like in this table, reader can more easily compare numbers one under another because hundreds are under hundreds, thousands under thousands and so on.<br /> <br /> There should be units declared for each column at least in header. However there were no units declared in original table so we cannot say what currency is the amount displayed in. However there was added % sign to each cell in percentage columns. It is a convention too. Reader sees that the number describes percentage without looking into header row.<br /> <br /> We changed also a format of the numbers, to make processing and comparing of numbers easier for reader. Comma was placed to the left of every three whole-number digits to divide thousands from millions, millions from billions, etc. Reader can more easily count digits in the number.<br /> <br /> Another change we made is addition of &quot;Education type&quot; into header row and removing of word &quot;Education&quot; from each row in first column. Thus the cells are shorter and don't have to be wrapped to two lines because of redundant information.<br /> <br /> -to delineate rows, every second line is filled with collor instead<br /> -row summary is shown under rule and in bold text<br /> -column summary is distinguished from other data by using border area around this summary<br /> -there is added white space between education type column and plan expenditure<br /> -white space is added also between columns describing plan expenditure and columns describing non-plan expenditure<br /> <br /> == Links ==<br /> <br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_2&diff=23190 2009-11-12T20:12:02Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]<br /> === Original table ===<br /> [[Image:expenditure-categ.JPG]]<br /> <br /> === Critic on original table ===<br /> <br /> === Redesigned table ===<br /> [[Image:expenditure-categ-repaired-2.png]]<br /> <br /> === Changes applied to table ===<br /> <br /> <br /> == Links ==<br /> <br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Expenditure-categ-repaired-2.png&diff=23189 2009-11-12T20:06:26Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_2&diff=23188 2009-11-12T20:06:00Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]<br /> === Zu beurteilende Tabelle ===<br /> [[Image:expenditure-categ.JPG]]<br /> <br /> [[Image:expenditure-categ-repaired-2.png]]<br /> <br /> == Links ==<br /> <br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_2&diff=23187 2009-11-12T18:21:44Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]<br /> === Zu beurteilende Tabelle ===<br /> [[Image:expenditure-categ.JPG]]<br /> <br /> [[Image:expenditure-categ-repaired.png]]<br /> <br /> == Links ==<br /> <br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Expenditure-categ-repaired.png&diff=23186 2009-11-12T18:20:44Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2009/10_-_Gruppe_13_-_Aufgabe_2&diff=23185 2009-11-12T18:19:56Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== Aufgabenstellung ==<br /> [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]<br /> === Zu beurteilende Tabelle ===<br /> [[Image:expenditure-categ.JPG]]<br /> <br /> [[Image:expenditure-categ-repaired.JPG]]<br /> <br /> == Links ==<br /> <br /> <br /> * [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]<br /> <br /> * [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]<br /> <br /> *[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22807 2009-11-05T21:13:16Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean'''[Mario Livio-2002-The Golden Ratio: The Story of Phi], '''medial section''', '''golden cut'''[Summerson John-1963-Heavenly Mansions], '''extreme and mean ratio'''[Euclid-book6] when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> [[Image:golden-ratio-graphical.png|right|thumb|upright|]]<br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> <br /> ----<br /> <br /> ===GEOMETRY AND MATHEMATICS===<br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> <br /> There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.<br /> <br /> {| cellpadding=&quot;1&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Pentagram<br /> !width=&quot;150&quot;|Golden rectangle<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Pentagram2.png|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Golden_rectangle.png|120px]]<br /> |- align=center<br /> |Image Illustrates the hidden golden ratio in the very special shape, '''pentagram'''. || A rectangle is a '''golden rectangle''' when the sides are in the 1:0,618 proportion.<br /> |}<br /> <br /> <br /> ----<br /> <br /> ===ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations. In the following table you can see few examples for all.<br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Mona-Liza<br /> !width=&quot;150&quot;|Aztek decorations<br /> !width=&quot;130&quot;|Credit cards<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:mona-liza.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:aztec.jpg|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:card.jpg|120px]]<br /> |- align=center<br /> | In Mona-Liza painting you can find many golden rectangles that together create golden spiral.|| The space between the two heads is exacly Phi times the width of the heads.[Brooker]|| if you measure a credit-card, the outcome would be a perfect golden rectangle.[Batterywholesaler]<br /> |}<br /> <br /> ----<br /> <br /> ===Architecture===<br /> <br /> There is many examples of golden ratio even in architecture. Architect were inspired by this &quot;sacred ratio&quot; already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.<br /> <br /> <br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Great Pyramid of Giza<br /> !width=&quot;150&quot;|Parthenon<br /> !width=&quot;130&quot;|Engineering Plaza<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:great-pyramid.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:parthenon.gif|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:polyplaza.jpg|120px]]<br /> |- align=center<br /> | The Great Pyramid has proportions designed according to golden ratio.[Samuel Obara]|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.[Samuel Obara]|| The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza.[Dr Knott, 1996-2005]<br /> |}<br /> <br /> <br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> <br /> ==REFERENCES==<br /> <br /> [Mario Livio-2002-The Golden Ratio: The Story of Phi]{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}<br /> <br /> [Summerson John-1963-Heavenly Mansions]Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;<br /> <br /> [Euclid-book6]Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Samuel Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> [Samuel Obara]http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=User_talk:UE-InfoVis0910_0827462&diff=22800 2009-11-05T21:01:11Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>==changes==<br /> I have made following changes to golden ratio page (just very abstract, because there were quite many of them):<br /> -Most of the page was reorganized.<br /> -Some chapters where destroyed because there was not enough content and parts of content moved to other chapters.<br /> -I added information about how the constant is calculated<br /> -I added some new images with examples and explanations<br /> -Pictures in chapters about particular applications of golden ratio were organized into tables, so they spend less place<br /> -I removed the name Golden ratio from the subchapter's headers because it is already given that it is all about it<br /> <br /> That is actually I think all.<br /> <br /> It would be nice if someone could organize references and links.</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22798 2009-11-05T20:59:36Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> [[Image:golden-ratio-graphical.png|right|thumb|upright|]]<br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> <br /> ----<br /> <br /> ===GEOMETRY AND MATHEMATICS===<br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> <br /> There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.<br /> <br /> {| cellpadding=&quot;1&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Pentagram<br /> !width=&quot;150&quot;|Golden rectangle<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Pentagram2.png|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Golden_rectangle.png|120px]]<br /> |- align=center<br /> |Image Illustrates the hidden golden ratio in the very special shape, '''pentagram'''. || A rectangle is a '''golden rectangle''' when the sides are in the 1:0,618 proportion.<br /> |}<br /> <br /> <br /> ----<br /> <br /> ===ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations. In the following table you can see few examples for all.<br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Mona-Liza<br /> !width=&quot;150&quot;|Aztek decorations<br /> !width=&quot;130&quot;|Credit cards<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:mona-liza.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:aztec.jpg|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:card.jpg|120px]]<br /> |- align=center<br /> | In Mona-Liza painting you can find many golden rectangles that together create golden spiral.|| The space between the two heads is exacly Phi times the width of the heads.[Brooker]|| if you measure a credit-card, the outcome would be a perfect golden rectangle.[Batterywholesaler]<br /> |}<br /> <br /> ----<br /> <br /> ===Architecture===<br /> <br /> There is many examples of golden ratio even in architecture. Architect were inspired by this &quot;sacred ratio&quot; already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.<br /> <br /> <br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Great Pyramid of Giza<br /> !width=&quot;150&quot;|Parthenon<br /> !width=&quot;130&quot;|Engineering Plaza<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:great-pyramid.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:parthenon.gif|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:polyplaza.jpg|120px]]<br /> |- align=center<br /> | The Great Pyramid has proportions designed according to golden ratio.[Samuel Obara]|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.[Samuel Obara]|| The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza.[Dr Knott, 1996-2005]<br /> |}<br /> <br /> <br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> <br /> ==REFERENCES==<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Samuel Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> [Samuel Obara]http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22784 2009-11-05T20:38:31Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> [[Image:golden-ratio-graphical.png|right|thumb|upright|]]<br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> <br /> ----<br /> <br /> ===GEOMETRY AND MATHEMATICS===<br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> <br /> There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.<br /> <br /> {| cellpadding=&quot;1&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Pentagram<br /> !width=&quot;150&quot;|Golden rectangle<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Pentagram2.png|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Golden_rectangle.png|120px]]<br /> |- align=center<br /> |Image Illustrates the hidden golden ratio in the very special shape, '''pentagram'''. || A rectangle is a '''golden rectangle''' when the sides are in the 1:0,618 proportion.<br /> |}<br /> <br /> <br /> ----<br /> <br /> ===ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations. In the following table you can see few examples for all.<br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Mona-Liza<br /> !width=&quot;150&quot;|Aztek decorations<br /> !width=&quot;130&quot;|Credit cards<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:mona-liza.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:aztec.jpg|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:card.jpg|120px]]<br /> |- align=center<br /> | In Mona-Liza painting you can find many golden rectangles that together create golden spiral.|| The space between the two heads is exacly Phi times the width of the heads.[Brooker]|| if you measure a credit-card, the outcome would be a perfect golden rectangle.[Batterywholesaler]<br /> |}<br /> <br /> ----<br /> <br /> ===Architecture===<br /> <br /> There is many examples of golden ratio even in architecture. Architect were inspired by this &quot;sacred ratio&quot; already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.<br /> <br /> <br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Great Pyramid of Giza<br /> !width=&quot;150&quot;|Parthenon<br /> !width=&quot;130&quot;|Engineering Plaza<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:great-pyramid.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:parthenon.gif|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:polyplaza.jpg|120px]]<br /> |- align=center<br /> | The Great Pyramid has proportions designed according to golden ratio.|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.|| The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza.[Dr Knott, 1996-2005]<br /> |}<br /> <br /> <br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22782 2009-11-05T20:37:27Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> [[Image:golden-ratio-graphical.png|right|thumb|upright|]]<br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> <br /> ----<br /> <br /> ===GEOMETRY AND MATHEMATICS===<br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> <br /> There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.<br /> <br /> {| cellpadding=&quot;1&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Pentagram<br /> !width=&quot;150&quot;|Golden rectangle<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Pentagram2.png|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Golden_rectangle.png|120px]]<br /> |- align=center<br /> |Image Illustrates the hidden golden ratio in the very special shape, '''pentagram'''. || A rectangle is a '''golden rectangle''' when the sides are in the 1:0,618 proportion.<br /> |}<br /> <br /> <br /> ----<br /> <br /> ===ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations. In the following table you can see few examples for all.<br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Mona-Liza<br /> !width=&quot;150&quot;|Aztek decorations<br /> !width=&quot;130&quot;|Credit cards<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:mona-liza.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:aztec.jpg|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:card.jpg|120px]]<br /> |- align=center<br /> | In Mona-Liza painting you can find many golden rectangles that together create golden spiral.|| The space between the two heads is exacly Phi times the width of the heads.[Brooker]|| if you measure a credit-card, the outcome would be a perfect golden rectangle.[Batterywholesaler]<br /> |}<br /> <br /> ----<br /> <br /> ===Architecture===<br /> <br /> There is many examples of golden ratio even in architecture. Architect were inspired by this &quot;sacred ratio&quot; already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.<br /> <br /> <br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Great Pyramid of Giza<br /> !width=&quot;150&quot;|Parthenon<br /> !width=&quot;130&quot;|Engineering Plaza<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:great-pyramid.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:parthenon.gif|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:polyplaza.jpg|width=220px]]<br /> |- align=center<br /> | The Great Pyramid has proportions designed according to golden ratio.|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.|| The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza.[Dr Knott, 1996-2005]<br /> |}<br /> <br /> <br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Parthenon.gif&diff=22781 2009-11-05T20:36:10Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Great-pyramid.gif&diff=22780 2009-11-05T20:35:08Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22779 2009-11-05T20:33:29Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> [[Image:golden-ratio-graphical.png|right|thumb|upright|]]<br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> <br /> ----<br /> <br /> ===GEOMETRY AND MATHEMATICS===<br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> <br /> There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.<br /> <br /> {| cellpadding=&quot;1&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Pentagram<br /> !width=&quot;150&quot;|Golden rectangle<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Pentagram2.png|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Golden_rectangle.png|120px]]<br /> |- align=center<br /> |Image Illustrates the hidden golden ratio in the very special shape, '''pentagram'''. || A rectangle is a '''golden rectangle''' when the sides are in the 1:0,618 proportion.<br /> |}<br /> <br /> <br /> ----<br /> <br /> ===ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations. In the following table you can see few examples for all.<br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Mona-Liza<br /> !width=&quot;150&quot;|Aztek decorations<br /> !width=&quot;130&quot;|Credit cards<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:mona-liza.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:aztec.jpg|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:card.jpg|120px]]<br /> |- align=center<br /> | In Mona-Liza painting you can find many golden rectangles that together create golden spiral.|| The space between the two heads is exacly Phi times the width of the heads.[Brooker]|| if you measure a credit-card, the outcome would be a perfect golden rectangle.[Batterywholesaler]<br /> |}<br /> <br /> ----<br /> <br /> ===Architecture===<br /> <br /> There is many examples of golden ratio even in architecture. Architect were inspired by this &quot;sacred ratio&quot; already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.<br /> <br /> <br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Great Pyramid of Giza<br /> !width=&quot;150&quot;|Parthenon<br /> !width=&quot;130&quot;|Engineering Plaza<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:great-pyramid.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:parthenon.jpg|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:polyplaza.jpg|120px]]<br /> |- align=center<br /> | The Great Pyramid has proportions designed according to golden ratio.|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.|| The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza.[Dr Knott, 1996-2005]<br /> |}<br /> <br /> <br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Mona-liza.gif&diff=22775 2009-11-05T20:15:22Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22773 2009-11-05T20:08:55Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> [[Image:golden-ratio-graphical.png|right|thumb|upright|]]<br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> <br /> ----<br /> <br /> ===GEOMETRY AND MATHEMATICS===<br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> <br /> There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.<br /> <br /> {| cellpadding=&quot;1&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Pentagram<br /> !width=&quot;150&quot;|Golden rectangle<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Pentagram2.png|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Golden_rectangle.png|120px]]<br /> |- align=center<br /> |Image Illustrates the hidden golden ratio in the very special shape, '''pentagram'''. || A rectangle is a '''golden rectangle''' when the sides are in the 1:0,618 proportion.<br /> |}<br /> <br /> <br /> ----<br /> <br /> ===ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations.<br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Mona-Liza<br /> !width=&quot;150&quot;|Aztek decorations<br /> !width=&quot;130&quot;|Credit cards<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:mona-liza.gif]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:aztec.jpg|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:card.jpg|120px]]<br /> |- align=center<br /> | In Mona-Liza painting you can find many golden rectangles that together create golden spiral.|| The space between the two heads is exacly Phi times the width of the heads.[Brooker]|| if you measure a credit-card, the outcome would be a perfect golden rectangle.[Batterywholesaler]<br /> |}<br /> <br /> ----<br /> <br /> ===Architecture===<br /> <br /> <br /> The California Polytechnic State University is planing to build a new Engineering Plaza. This new construction is based on the Fibonacci numbers. The whole plan also bases on some shapes, which can be used to show the meaning of the golden ratio. The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza. Below you can see, what the plaza should look like.<br /> <br /> &lt;center&gt;<br /> [[Image:polyplaza.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> ----<br /> <br /> ==CONCLUSION==<br /> <br /> The very simple and suitable conclusion is that the Golden Ratio can be found everywhere. In probably any field you can think of. And in many, not all, but at least very many cases, the Golden Ratio is used to improve something. Some don't even know, that something they have created respects the laws of the Golden Ratio. This is kind of like the ancient egyptians, who probably used the Golden Ratio, but never thought of, and so never really discovered it.<br /> <br /> <br /> '''So look for it, maybe you can discover an ancient theory in something quite modern...'''<br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22770 2009-11-05T19:55:20Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> [[Image:golden-ratio-graphical.png|right|thumb|upright|]]<br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> ----<br /> <br /> ===GEOMETRY AND MATHEMATICS===<br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> <br /> There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.<br /> <br /> {| cellpadding=&quot;1&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Pentagram<br /> !width=&quot;150&quot;|Golden rectangle<br /> |- align=center<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Pentagram2.png|120px]]<br /> | style=&quot;border:1px solid;&quot;|<br /> [[Image:Golden_rectangle.png|120px]]<br /> |- align=center<br /> |Image Illustrates the hidden golden ratio in the very special shape, '''pentagram'''. || A rectangle is a '''golden rectangle''' when the sides are in the 1:0,618 proportion.<br /> |}<br /> <br /> ----<br /> <br /> ===ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations.<br /> {| cellpadding=&quot;2&quot; style=&quot;border:1px solid darkgray;&quot;<br /> !width=&quot;140&quot;|Left<br /> !width=&quot;150&quot;|Middle<br /> !width=&quot;130&quot;|Right<br /> |- align=center<br /> | style=&quot;border:1px solid blue;&quot;|<br /> [[Image:StarIconBronze.png|120px]]<br /> | style=&quot;border:1px solid #777777;&quot;|<br /> [[Image:StarIconGold.png|120px|Caption when mouse-over image]]<br /> | style=&quot;border:1px solid #22AA55;&quot;|&lt;!--greenish border--&gt;<br /> [[Image:StarIconGreen.png|120px|Green stellar icon]]<br /> |- align=center<br /> |Bronze star || Gold star || Green star<br /> |}<br /> <br /> <br /> <br /> {{Quotation|... Many books claim that if you draw a rechtangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of the rectangle is equal to the Golden Ratio ...| Mario Livio, November 2002}} <br /> <br /> <br /> &lt;center&gt;<br /> The evidence of the golden ratio was proved on many different creations, like the Aztek decorations below:<br /> <br /> [[Image:aztec.jpg]]<br /> <br /> [Brooker]<br /> <br /> <br /> '''The space between the two heads is exacly Phi times the width of the heads.'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> The California Polytechnic State University is planing to build a new Engineering Plaza. This new construction is based on the Fibonacci numbers. The whole plan also bases on some shapes, which can be used to show the meaning of the golden ratio. The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza. Below you can see, what the plaza should look like.<br /> <br /> &lt;center&gt;<br /> [[Image:polyplaza.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> &lt;/center&gt;<br /> <br /> <br /> Even the mountainbike shown below, has the golden ratio built in. Take a look at the image, and the marked golden sections of the bike. <br /> <br /> <br /> &lt;center&gt;<br /> [[Image:bike.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> <br /> <br /> '''Mountainbike Trek Fuel 90 (belongs to Brian Agron of Fairfax)'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> So the use of the golden ratio can not only be found in ancient paintings and sculptures, but also in the stunning creations still to come.<br /> <br /> <br /> {||<br /> |[[Image:card.jpg]] <br /> |valign=top|<br /> Did you know, that if you measure a credit-card, the outcome would be a perfect golden rectangle. This ofcourse shows, that the golden ratio is very well in use. Even if it comes to the proportions and masses of everyday things like credit cards. '''[Batterywholesaler]'''<br /> |}<br /> <br /> ----<br /> <br /> ===Architecture===<br /> <br /> ----<br /> <br /> ==CONCLUSION==<br /> <br /> The very simple and suitable conclusion is that the Golden Ratio can be found everywhere. In probably any field you can think of. And in many, not all, but at least very many cases, the Golden Ratio is used to improve something. Some don't even know, that something they have created respects the laws of the Golden Ratio. This is kind of like the ancient egyptians, who probably used the Golden Ratio, but never thought of, and so never really discovered it.<br /> <br /> <br /> '''So look for it, maybe you can discover an ancient theory in something quite modern...'''<br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Golden-ratio-graphical.png&diff=22768 2009-11-05T19:36:49Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22767 2009-11-05T19:36:34Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> [[Image:golden-ratio-graphical.png|right|thumb|upright|]]<br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> ----<br /> <br /> ===GEOMETRY AND MATHEMATICS===<br /> <br /> [[Image:Golden_rectangle.png|right|thumb|upright|A rectangle is a '''golden rectangle''' when the sides are in the 1:0,618 proportion.]]<br /> [[Image:Pentagram2.png|right|thumb|upright|Image Illustrates the hidden golden ratio in the very special shape, '''pentagram'''.]]<br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.<br /> <br /> ----<br /> <br /> ===ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations.<br /> <br /> <br /> {{Quotation|... Many books claim that if you draw a rechtangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of the rectangle is equal to the Golden Ratio ...| Mario Livio, November 2002}} <br /> <br /> <br /> &lt;center&gt;<br /> The evidence of the golden ratio was proved on many different creations, like the Aztek decorations below:<br /> <br /> [[Image:aztec.jpg]]<br /> <br /> [Brooker]<br /> <br /> <br /> '''The space between the two heads is exacly Phi times the width of the heads.'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> The California Polytechnic State University is planing to build a new Engineering Plaza. This new construction is based on the Fibonacci numbers. The whole plan also bases on some shapes, which can be used to show the meaning of the golden ratio. The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza. Below you can see, what the plaza should look like.<br /> <br /> &lt;center&gt;<br /> [[Image:polyplaza.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> &lt;/center&gt;<br /> <br /> <br /> Even the mountainbike shown below, has the golden ratio built in. Take a look at the image, and the marked golden sections of the bike. <br /> <br /> <br /> &lt;center&gt;<br /> [[Image:bike.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> <br /> <br /> '''Mountainbike Trek Fuel 90 (belongs to Brian Agron of Fairfax)'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> So the use of the golden ratio can not only be found in ancient paintings and sculptures, but also in the stunning creations still to come.<br /> <br /> <br /> {||<br /> |[[Image:card.jpg]] <br /> |valign=top|<br /> Did you know, that if you measure a credit-card, the outcome would be a perfect golden rectangle. This ofcourse shows, that the golden ratio is very well in use. Even if it comes to the proportions and masses of everyday things like credit cards. '''[Batterywholesaler]'''<br /> |}<br /> <br /> ----<br /> <br /> ===Architecture===<br /> <br /> ----<br /> <br /> ==CONCLUSION==<br /> <br /> The very simple and suitable conclusion is that the Golden Ratio can be found everywhere. In probably any field you can think of. And in many, not all, but at least very many cases, the Golden Ratio is used to improve something. Some don't even know, that something they have created respects the laws of the Golden Ratio. This is kind of like the ancient egyptians, who probably used the Golden Ratio, but never thought of, and so never really discovered it.<br /> <br /> <br /> '''So look for it, maybe you can discover an ancient theory in something quite modern...'''<br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22766 2009-11-05T19:30:27Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN GEOMETRY AND MATHEMATICS===<br /> <br /> [[Image:Golden_rectangle.png|right|thumb|upright|A rectangle is a '''golden rectangle''' when the sides are in the 1:0,618 proportion.]]<br /> [[Image:Pentagram2.png|right|thumb|upright|Image Illustrates the hidden golden ratio in the very special shape, '''pentagram'''.]]<br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations.<br /> <br /> <br /> {{Quotation|... Many books claim that if you draw a rechtangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of the rectangle is equal to the Golden Ratio ...| Mario Livio, November 2002}} <br /> <br /> <br /> &lt;center&gt;<br /> The evidence of the golden ratio was proved on many different creations, like the Aztek decorations below:<br /> <br /> [[Image:aztec.jpg]]<br /> <br /> [Brooker]<br /> <br /> <br /> '''The space between the two heads is exacly Phi times the width of the heads.'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> The California Polytechnic State University is planing to build a new Engineering Plaza. This new construction is based on the Fibonacci numbers. The whole plan also bases on some shapes, which can be used to show the meaning of the golden ratio. The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza. Below you can see, what the plaza should look like.<br /> <br /> &lt;center&gt;<br /> [[Image:polyplaza.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> &lt;/center&gt;<br /> <br /> <br /> Even the mountainbike shown below, has the golden ratio built in. Take a look at the image, and the marked golden sections of the bike. <br /> <br /> <br /> &lt;center&gt;<br /> [[Image:bike.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> <br /> <br /> '''Mountainbike Trek Fuel 90 (belongs to Brian Agron of Fairfax)'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> So the use of the golden ratio can not only be found in ancient paintings and sculptures, but also in the stunning creations still to come.<br /> <br /> <br /> {||<br /> |[[Image:card.jpg]] <br /> |valign=top|<br /> Did you know, that if you measure a credit-card, the outcome would be a perfect golden rectangle. This ofcourse shows, that the golden ratio is very well in use. Even if it comes to the proportions and masses of everyday things like credit cards. '''[Batterywholesaler]'''<br /> |}<br /> <br /> ----<br /> <br /> ==CONCLUSION==<br /> <br /> The very simple and suitable conclusion is that the Golden Ratio can be found everywhere. In probably any field you can think of. And in many, not all, but at least very many cases, the Golden Ratio is used to improve something. Some don't even know, that something they have created respects the laws of the Golden Ratio. This is kind of like the ancient egyptians, who probably used the Golden Ratio, but never thought of, and so never really discovered it.<br /> <br /> <br /> '''So look for it, maybe you can discover an ancient theory in something quite modern...'''<br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Fibonacci-example-2.png&diff=22761 2009-11-05T19:06:04Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22760 2009-11-05T19:05:47Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> ----<br /> <br /> ===HISTORY===<br /> <br /> <br /> The Golden ratio can be found as far back to the building of the Great Pyramid of Giza around 2560 BC. <br /> <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> Even Plato, the Greek Philosopher was occupied by the Golden ratio.<br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN GEOMETRY AND MATHEMATICS===<br /> <br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]]<br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-2.png]]<br /> <br /> <br /> '''The Golden Ratio''' can also be found in different kinds of shapes. This goes on from the usual rechangle, through different kinds of triangles and to the very complicated shapes like the pentacle.<br /> <br /> <br /> A rectanle is a Golden rectangle when the sides are in the 1:0,618 proportion. Below is an example of this kind of shape.<br /> <br /> [[Image:Golden_rectangle.png]]<br /> <br /> [Wikipedia, Golden rectangle, 2005]<br /> <br /> <br /> <br /> Another shape where the golden ratio can be found is the Pentagramm. This image below, illustrates the hidden golden ratio in this very special shape.<br /> <br /> [[Image:Pentagram2.png]]<br /> <br /> [Wikipedia, Pentagram, 2005]<br /> <br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations.<br /> <br /> <br /> {{Quotation|... Many books claim that if you draw a rechtangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of the rectangle is equal to the Golden Ratio ...| Mario Livio, November 2002}} <br /> <br /> <br /> &lt;center&gt;<br /> The evidence of the golden ratio was proved on many different creations, like the Aztek decorations below:<br /> <br /> [[Image:aztec.jpg]]<br /> <br /> [Brooker]<br /> <br /> <br /> '''The space between the two heads is exacly Phi times the width of the heads.'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> The California Polytechnic State University is planing to build a new Engineering Plaza. This new construction is based on the Fibonacci numbers. The whole plan also bases on some shapes, which can be used to show the meaning of the golden ratio. The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza. Below you can see, what the plaza should look like.<br /> <br /> &lt;center&gt;<br /> [[Image:polyplaza.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> &lt;/center&gt;<br /> <br /> <br /> Even the mountainbike shown below, has the golden ratio built in. Take a look at the image, and the marked golden sections of the bike. <br /> <br /> <br /> &lt;center&gt;<br /> [[Image:bike.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> <br /> <br /> '''Mountainbike Trek Fuel 90 (belongs to Brian Agron of Fairfax)'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> So the use of the golden ratio can not only be found in ancient paintings and sculptures, but also in the stunning creations still to come.<br /> <br /> <br /> {||<br /> |[[Image:card.jpg]] <br /> |valign=top|<br /> Did you know, that if you measure a credit-card, the outcome would be a perfect golden rectangle. This ofcourse shows, that the golden ratio is very well in use. Even if it comes to the proportions and masses of everyday things like credit cards. '''[Batterywholesaler]'''<br /> |}<br /> <br /> ----<br /> <br /> ==CONCLUSION==<br /> <br /> The very simple and suitable conclusion is that the Golden Ratio can be found everywhere. In probably any field you can think of. And in many, not all, but at least very many cases, the Golden Ratio is used to improve something. Some don't even know, that something they have created respects the laws of the Golden Ratio. This is kind of like the ancient egyptians, who probably used the Golden Ratio, but never thought of, and so never really discovered it.<br /> <br /> <br /> '''So look for it, maybe you can discover an ancient theory in something quite modern...'''<br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Fibonacci-example-1.png&diff=22758 2009-11-05T19:04:46Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22756 2009-11-05T19:03:57Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> ----<br /> <br /> ===HISTORY===<br /> <br /> <br /> The Golden ratio can be found as far back to the building of the Great Pyramid of Giza around 2560 BC. <br /> <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> Even Plato, the Greek Philosopher was occupied by the Golden ratio.<br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN GEOMETRY AND MATHEMATICS===<br /> <br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignment equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it. These are the relationships between the larger and smaller numbers in the golden ratio. Below you can see example for division of bigger by smaller number:<br /> <br /> [[Image:fibonacci-example-1.png]] and <br /> <br /> and by smaller devided by bigger number:<br /> <br /> [[Image:fibonacci-example-1.png]] and <br /> <br /> <br /> '''The Golden Ratio''' can also be found in different kinds of shapes. This goes on from the usual rechangle, through different kinds of triangles and to the very complicated shapes like the pentacle.<br /> <br /> <br /> A rectanle is a Golden rectangle when the sides are in the 1:0,618 proportion. Below is an example of this kind of shape.<br /> <br /> [[Image:Golden_rectangle.png]]<br /> <br /> [Wikipedia, Golden rectangle, 2005]<br /> <br /> <br /> <br /> Another shape where the golden ratio can be found is the Pentagramm. This image below, illustrates the hidden golden ratio in this very special shape.<br /> <br /> [[Image:Pentagram2.png]]<br /> <br /> [Wikipedia, Pentagram, 2005]<br /> <br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations.<br /> <br /> <br /> {{Quotation|... Many books claim that if you draw a rechtangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of the rectangle is equal to the Golden Ratio ...| Mario Livio, November 2002}} <br /> <br /> <br /> &lt;center&gt;<br /> The evidence of the golden ratio was proved on many different creations, like the Aztek decorations below:<br /> <br /> [[Image:aztec.jpg]]<br /> <br /> [Brooker]<br /> <br /> <br /> '''The space between the two heads is exacly Phi times the width of the heads.'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> The California Polytechnic State University is planing to build a new Engineering Plaza. This new construction is based on the Fibonacci numbers. The whole plan also bases on some shapes, which can be used to show the meaning of the golden ratio. The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza. Below you can see, what the plaza should look like.<br /> <br /> &lt;center&gt;<br /> [[Image:polyplaza.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> &lt;/center&gt;<br /> <br /> <br /> Even the mountainbike shown below, has the golden ratio built in. Take a look at the image, and the marked golden sections of the bike. <br /> <br /> <br /> &lt;center&gt;<br /> [[Image:bike.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> <br /> <br /> '''Mountainbike Trek Fuel 90 (belongs to Brian Agron of Fairfax)'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> So the use of the golden ratio can not only be found in ancient paintings and sculptures, but also in the stunning creations still to come.<br /> <br /> <br /> {||<br /> |[[Image:card.jpg]] <br /> |valign=top|<br /> Did you know, that if you measure a credit-card, the outcome would be a perfect golden rectangle. This ofcourse shows, that the golden ratio is very well in use. Even if it comes to the proportions and masses of everyday things like credit cards. '''[Batterywholesaler]'''<br /> |}<br /> <br /> ----<br /> <br /> ==CONCLUSION==<br /> <br /> The very simple and suitable conclusion is that the Golden Ratio can be found everywhere. In probably any field you can think of. And in many, not all, but at least very many cases, the Golden Ratio is used to improve something. Some don't even know, that something they have created respects the laws of the Golden Ratio. This is kind of like the ancient egyptians, who probably used the Golden Ratio, but never thought of, and so never really discovered it.<br /> <br /> <br /> '''So look for it, maybe you can discover an ancient theory in something quite modern...'''<br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22753 2009-11-05T18:44:52Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design. <br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> ----<br /> <br /> ===HISTORY===<br /> <br /> <br /> The Golden ratio can be found as far back to the building of the Great Pyramid of Giza around 2560 BC. <br /> <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> Even Plato, the Greek Philosopher was occupied by the Golden ratio.<br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN GEOMETRY AND MATHEMATICS===<br /> <br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignement equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it.<br /> <br /> <br /> These are the relationships between the larger and smaller numbers in the golden ratio.<br /> <br /> <br /> Below you can find an example of the Fibonacci-Numbers<br /> <br /> [[Image:fibonacci.jpg]]<br /> <br /> [Kaphammel, 2000]<br /> <br /> <br /> <br /> '''The Golden Ratio''' can also be found in different kinds of shapes. This goes on from the usual rechangle, through different kinds of triangles and to the very complicated shapes like the pentacle.<br /> <br /> <br /> A rectanle is a Golden rectangle when the sides are in the 1:0,618 proportion. Below is an example of this kind of shape.<br /> <br /> [[Image:Golden_rectangle.png]]<br /> <br /> [Wikipedia, Golden rectangle, 2005]<br /> <br /> <br /> <br /> Another shape where the golden ratio can be found is the Pentagramm. This image below, illustrates the hidden golden ratio in this very special shape.<br /> <br /> [[Image:Pentagram2.png]]<br /> <br /> [Wikipedia, Pentagram, 2005]<br /> <br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations.<br /> <br /> <br /> {{Quotation|... Many books claim that if you draw a rechtangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of the rectangle is equal to the Golden Ratio ...| Mario Livio, November 2002}} <br /> <br /> <br /> &lt;center&gt;<br /> The evidence of the golden ratio was proved on many different creations, like the Aztek decorations below:<br /> <br /> [[Image:aztec.jpg]]<br /> <br /> [Brooker]<br /> <br /> <br /> '''The space between the two heads is exacly Phi times the width of the heads.'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> The California Polytechnic State University is planing to build a new Engineering Plaza. This new construction is based on the Fibonacci numbers. The whole plan also bases on some shapes, which can be used to show the meaning of the golden ratio. The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza. Below you can see, what the plaza should look like.<br /> <br /> &lt;center&gt;<br /> [[Image:polyplaza.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> &lt;/center&gt;<br /> <br /> <br /> Even the mountainbike shown below, has the golden ratio built in. Take a look at the image, and the marked golden sections of the bike. <br /> <br /> <br /> &lt;center&gt;<br /> [[Image:bike.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> <br /> <br /> '''Mountainbike Trek Fuel 90 (belongs to Brian Agron of Fairfax)'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> So the use of the golden ratio can not only be found in ancient paintings and sculptures, but also in the stunning creations still to come.<br /> <br /> <br /> {||<br /> |[[Image:card.jpg]] <br /> |valign=top|<br /> Did you know, that if you measure a credit-card, the outcome would be a perfect golden rectangle. This ofcourse shows, that the golden ratio is very well in use. Even if it comes to the proportions and masses of everyday things like credit cards. '''[Batterywholesaler]'''<br /> |}<br /> <br /> ----<br /> <br /> ==CONCLUSION==<br /> <br /> The very simple and suitable conclusion is that the Golden Ratio can be found everywhere. In probably any field you can think of. And in many, not all, but at least very many cases, the Golden Ratio is used to improve something. Some don't even know, that something they have created respects the laws of the Golden Ratio. This is kind of like the ancient egyptians, who probably used the Golden Ratio, but never thought of, and so never really discovered it.<br /> <br /> <br /> '''So look for it, maybe you can discover an ancient theory in something quite modern...'''<br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22750 2009-11-05T18:37:20Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> <br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> <br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> <br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> <br /> [[Image:golden-ratio-4.png]]<br /> <br /> ----<br /> <br /> ===INTRODUCTION===<br /> <br /> <br /> The use of the golden ratio can be found in many different fields. In mathematics, architecture, geometry, science, biology, nature, art, design and many others. <br /> <br /> Other names of this word are as follows: the '''golden mean''',''' golden section''', '''golden number''', '''divine proportion''' or '''sectio divina'''(golden Cut).<br /> <br /> ----<br /> <br /> ===HISTORY===<br /> <br /> <br /> The Golden ratio can be found as far back to the building of the Great Pyramid of Giza around 2560 BC. <br /> <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> Even Plato, the Greek Philosopher was occupied by the Golden ratio.<br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN GEOMETRY AND MATHEMATICS===<br /> <br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignement equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it.<br /> <br /> <br /> These are the relationships between the larger and smaller numbers in the golden ratio.<br /> <br /> <br /> Below you can find an example of the Fibonacci-Numbers<br /> <br /> [[Image:fibonacci.jpg]]<br /> <br /> [Kaphammel, 2000]<br /> <br /> <br /> <br /> '''The Golden Ratio''' can also be found in different kinds of shapes. This goes on from the usual rechangle, through different kinds of triangles and to the very complicated shapes like the pentacle.<br /> <br /> <br /> A rectanle is a Golden rectangle when the sides are in the 1:0,618 proportion. Below is an example of this kind of shape.<br /> <br /> [[Image:Golden_rectangle.png]]<br /> <br /> [Wikipedia, Golden rectangle, 2005]<br /> <br /> <br /> <br /> Another shape where the golden ratio can be found is the Pentagramm. This image below, illustrates the hidden golden ratio in this very special shape.<br /> <br /> [[Image:Pentagram2.png]]<br /> <br /> [Wikipedia, Pentagram, 2005]<br /> <br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations.<br /> <br /> <br /> {{Quotation|... Many books claim that if you draw a rechtangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of the rectangle is equal to the Golden Ratio ...| Mario Livio, November 2002}} <br /> <br /> <br /> &lt;center&gt;<br /> The evidence of the golden ratio was proved on many different creations, like the Aztek decorations below:<br /> <br /> [[Image:aztec.jpg]]<br /> <br /> [Brooker]<br /> <br /> <br /> '''The space between the two heads is exacly Phi times the width of the heads.'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> The California Polytechnic State University is planing to build a new Engineering Plaza. This new construction is based on the Fibonacci numbers. The whole plan also bases on some shapes, which can be used to show the meaning of the golden ratio. The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza. Below you can see, what the plaza should look like.<br /> <br /> &lt;center&gt;<br /> [[Image:polyplaza.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> &lt;/center&gt;<br /> <br /> <br /> Even the mountainbike shown below, has the golden ratio built in. Take a look at the image, and the marked golden sections of the bike. <br /> <br /> <br /> &lt;center&gt;<br /> [[Image:bike.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> <br /> <br /> '''Mountainbike Trek Fuel 90 (belongs to Brian Agron of Fairfax)'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> So the use of the golden ratio can not only be found in ancient paintings and sculptures, but also in the stunning creations still to come.<br /> <br /> <br /> {||<br /> |[[Image:card.jpg]] <br /> |valign=top|<br /> Did you know, that if you measure a credit-card, the outcome would be a perfect golden rectangle. This ofcourse shows, that the golden ratio is very well in use. Even if it comes to the proportions and masses of everyday things like credit cards. '''[Batterywholesaler]'''<br /> |}<br /> <br /> ----<br /> <br /> ==CONCLUSION==<br /> <br /> The very simple and suitable conclusion is that the Golden Ratio can be found everywhere. In probably any field you can think of. And in many, not all, but at least very many cases, the Golden Ratio is used to improve something. Some don't even know, that something they have created respects the laws of the Golden Ratio. This is kind of like the ancient egyptians, who probably used the Golden Ratio, but never thought of, and so never really discovered it.<br /> <br /> <br /> '''So look for it, maybe you can discover an ancient theory in something quite modern...'''<br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=Golden_Ratio&diff=22749 2009-11-05T18:35:30Z

<p>UE-InfoVis0910 0827462: </p> <hr /> <div>== GOLDEN RATIO ==<br /> <br /> <br /> <br /> ----<br /> ===DEFINITION===<br /> It is said that two quantities are in a golden ratio also known under names '''golden section''', '''golden mean''' &lt;ref name=&quot;livio&quot;&gt;{{cite book|last=Livio|first=Mario|year=2002|title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number|publisher=Broadway Books|location=New York|isbn=0-7679-0815-5}}&lt;/ref&gt;, '''medial section''', '''golden cut''' &lt;ref&gt;Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. &quot;And the same applies in architecture, to the [[rectangle]]s representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design.&quot;&lt;/ref&gt;, '''extreme and mean ratio''' &lt;ref name=&quot;Elements 6.3&quot;&gt;Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.&lt;/ref&gt; when the following, expressed in algebraic form, is true:<br /> <br /> [[Image:golden-ratio.png]]<br /> <br /> In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).<br /> <br /> ----<br /> <br /> ===CALCULATION===<br /> <br /> Method for calculation of golden ratio constant is beginning from the following algebraic formula:<br /> [[Image:golden-ratio.png]]<br /> <br /> From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:<br /> [[Image:golden-ratio-1.png]]<br /> <br /> Devided by b formula changes to:<br /> [[Image:golden-ratio-2.png]]<br /> <br /> Now we need to multiply formula by [[Image:Phi.png]] and by moving content of the right side to the left side we get quadratic equation:<br /> [[Image:golden-ratio-3.png]]<br /> <br /> The only positive result to above equation is the irrational number we have already presented:<br /> [[Image:golden-ratio-4.png]]<br /> <br /> ----<br /> <br /> ===INTRODUCTION===<br /> <br /> <br /> The use of the golden ratio can be found in many different fields. In mathematics, architecture, geometry, science, biology, nature, art, design and many others. <br /> <br /> Other names of this word are as follows: the '''golden mean''',''' golden section''', '''golden number''', '''divine proportion''' or '''sectio divina'''(golden Cut).<br /> <br /> ----<br /> <br /> ===HISTORY===<br /> <br /> <br /> The Golden ratio can be found as far back to the building of the Great Pyramid of Giza around 2560 BC. <br /> <br /> <br /> The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.<br /> <br /> {{Quotation|A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.| Euclid of Alexandria(ca. 300BC)}} <br /> <br /> Even Plato, the Greek Philosopher was occupied by the Golden ratio.<br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN GEOMETRY AND MATHEMATICS===<br /> <br /> <br /> Fibonacci introduced to us, the Fibonacci-Numbers:<br /> <br /> 1,2,3,5,8,13,21,34,55,89,144,233,377,....<br /> <br /> <br /> Every number of this alignement equals to 0,168 if you divide it with the one before it, and 1,618 when you divide it with the number after it.<br /> <br /> <br /> These are the relationships between the larger and smaller numbers in the golden ratio.<br /> <br /> <br /> Below you can find an example of the Fibonacci-Numbers<br /> <br /> [[Image:fibonacci.jpg]]<br /> <br /> [Kaphammel, 2000]<br /> <br /> <br /> <br /> '''The Golden Ratio''' can also be found in different kinds of shapes. This goes on from the usual rechangle, through different kinds of triangles and to the very complicated shapes like the pentacle.<br /> <br /> <br /> A rectanle is a Golden rectangle when the sides are in the 1:0,618 proportion. Below is an example of this kind of shape.<br /> <br /> [[Image:Golden_rectangle.png]]<br /> <br /> [Wikipedia, Golden rectangle, 2005]<br /> <br /> <br /> <br /> Another shape where the golden ratio can be found is the Pentagramm. This image below, illustrates the hidden golden ratio in this very special shape.<br /> <br /> [[Image:Pentagram2.png]]<br /> <br /> [Wikipedia, Pentagram, 2005]<br /> <br /> <br /> ----<br /> <br /> ===GOLDEN RATIO IN ART &amp; DESIGN===<br /> <br /> <br /> Since the beginning of ART &amp; Design, the artist and designers used the golden ratio in order to manage and achieve beauty and balance in their creations.<br /> <br /> <br /> {{Quotation|... Many books claim that if you draw a rechtangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of the rectangle is equal to the Golden Ratio ...| Mario Livio, November 2002}} <br /> <br /> <br /> &lt;center&gt;<br /> The evidence of the golden ratio was proved on many different creations, like the Aztek decorations below:<br /> <br /> [[Image:aztec.jpg]]<br /> <br /> [Brooker]<br /> <br /> <br /> '''The space between the two heads is exacly Phi times the width of the heads.'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> The California Polytechnic State University is planing to build a new Engineering Plaza. This new construction is based on the Fibonacci numbers. The whole plan also bases on some shapes, which can be used to show the meaning of the golden ratio. The Designers of this new Plaza have chosen the Fibonacci series spiral, or also called the golden mean to design this new state of the art plaza. Below you can see, what the plaza should look like.<br /> <br /> &lt;center&gt;<br /> [[Image:polyplaza.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> &lt;/center&gt;<br /> <br /> <br /> Even the mountainbike shown below, has the golden ratio built in. Take a look at the image, and the marked golden sections of the bike. <br /> <br /> <br /> &lt;center&gt;<br /> [[Image:bike.jpg]]<br /> <br /> [Dr Knott, 1996-2005]<br /> <br /> <br /> '''Mountainbike Trek Fuel 90 (belongs to Brian Agron of Fairfax)'''<br /> &lt;/center&gt;<br /> <br /> <br /> <br /> So the use of the golden ratio can not only be found in ancient paintings and sculptures, but also in the stunning creations still to come.<br /> <br /> <br /> {||<br /> |[[Image:card.jpg]] <br /> |valign=top|<br /> Did you know, that if you measure a credit-card, the outcome would be a perfect golden rectangle. This ofcourse shows, that the golden ratio is very well in use. Even if it comes to the proportions and masses of everyday things like credit cards. '''[Batterywholesaler]'''<br /> |}<br /> <br /> ----<br /> <br /> ==CONCLUSION==<br /> <br /> The very simple and suitable conclusion is that the Golden Ratio can be found everywhere. In probably any field you can think of. And in many, not all, but at least very many cases, the Golden Ratio is used to improve something. Some don't even know, that something they have created respects the laws of the Golden Ratio. This is kind of like the ancient egyptians, who probably used the Golden Ratio, but never thought of, and so never really discovered it.<br /> <br /> <br /> '''So look for it, maybe you can discover an ancient theory in something quite modern...'''<br /> ----<br /> <br /> == Related Links ==<br /> *[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]<br /> *[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]<br /> <br /> ==REFERENCES==<br /> <br /> <br /> [Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio<br /> <br /> [Absoluteastronomy] Absoluteastronomy, Golden Ratio, http://www.absoluteastronomy.com/encyclopedia/g/go/golden_ratio.htm<br /> <br /> [Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000<br /> <br /> [Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle<br /> <br /> [Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram<br /> <br /> [Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html<br /> <br /> [Dr Knott, 1996-2005] Dr Ron Knott, Fibonacci Numbers and The Golden Section in Art, Architecture and Music, University of Surrey, 1996-2005, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html<br /> <br /> [Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images<br /> <br /> [Obara] Samuel Obara, Golden Ratio in Art and Architecture, University of Georgia, http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html<br /> <br /> [Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/<br /> <br /> <br /> <br /> [[Category:Glossary]]</div>

UE-InfoVis0910 0827462 https://infovis-wiki.net/w/index.php?title=File:Golden-ratio-4.png&diff=22748 2009-11-05T18:24:21Z

<p>UE-InfoVis0910 0827462: New page: == Summary == == Copyright status == == Source ==</p> <hr /> <div>== Summary ==<br /> <br /> == Copyright status ==<br /> <br /> == Source ==</div>

UE-InfoVis0910 0827462