InfoVis:Wiki - User contributions [en]

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 4

2010-01-06T18:15:10Z

UE-InfoVis0910 0251293:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]
=== Zu erstellende Visualisierung ===
-------------------------------
* Stammbaum der Nachkommen von Lisa und Bart Simpson*

...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.

Die Visualisierung soll folgende Informationen darstellen:

- Verwandtschaftsverhältnisse (zumindest Eltern-Kinder),

- Unterscheidung zwischen Blutsverwandtschaft und angeheirateten Familienmitgliedern,

- Geburts- und Todestag sowie Lebensdauer von allen Familienmitgliedern,

- wichtige Ereignisse im Leben jedes Familienmitglieds (z.B., Anzeigen, Gefängnisaufenthalte, Schulzeit, Studienzeit, Nobelpreise, Arbeitslosigkeit etc.)

- Zufriedenheit jedes Familienmitglieds (Skala: sehr niedrig - niedrig - mittel - hoch - sehr hoch); kann sich im Laufe des Lebens ändern.

Die Visualisierung soll die interaktive Auseinandersetzung mit den Daten ermöglichen.
Verpflichtend:
Möglichkeiten zum besseren Vergleich von einzelnen Abschnitten der Stammbäume bzw. Vergleich von Ausschnitten aus Lisas und Barts Stammbäumen.
+ mind. 2 weitere Interaktionsmöglichkeiten (z.B., Details on Demand, Filteroptionen)

Allgemein:

- Die Daten sollen zur Analyse von Zusammenhängen zwischen Familienverhältnissen, wichtigen Ereignissen und Zufriedenheit visualisiert werden (die Anwendungsgebiets- und Zielgruppenanalyse kann kurz gehalten werden).

- 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).

- Die Mockups sollten zumindest 1) die beiden Stammbäume im Überblick und 2) eine detaillierte Vergleichsansicht von 2 Teil-Stammbäumen wiedergeben.

- Alle nicht angeführten Daten können frei erfunden werden.
===Area of application===
------------------------------

===Data set analysis===
------------------------------

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.

====Family Relationship====
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.

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.

====Difference between blood and by marriage relatives====
This requires 3-dimensional structure. First dimension and second dimension contains members of family and third describes the type of relationship where relationship exists.

Value is logical true/false value assigned to relationship between two people.

====Length of life====
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.

The value describing length of life is discrete and numerical, e.g. 40 years.

====Date of birth and day of death====
As well as length of life is this information also simple 1-dimensional data structure.
Data are discrete and ordinal, e.g. 20. January 1990.

====Content (happiness)====
Content of person in particular parts of life is temporal structure.

The content is ordinal discrete value from following possibilities (ordered from best to worse):
* very high
* high
* middle
* low
* very low
Time is defined in intervals to which person has one of introduced content levels assigned.

====Important events in life====
The last information is also temporal structure.

In comparison to "content", the "important events in life" is nominal discrete value. Particular values could be "graduation", "Nobel price for peace", "imprisoned", etc. Events are assigned to intervals or instants, i.e. "graduation" can be assigned to instant 20. May 1990, but "imprisoned" will be assigned to interval 20. May 1990 - 20. May 1995.

====Graduate====

This is a boolean value with yes when graduated or no if not.

===Target audience===
------------------------------
Despite the fact that The Simpsons is cartoon, its audience consists mainly of adults. According to "The Simpsons, Innovation and Tradition in a Postmodern TV Family"[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.

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.

===Purpose of visualization===
------------------------------
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.

===Mockup===

====Overview====
[[Image:overview.png]]

====Detail of a Subtree and Member====
With mouseover you can get through subtrees. When you click on a member a detail of a member will popup.

[[Image:subtree-detail.png]]

====Subtree Selection for Comparison====
With Ctrl + click you can select subtrees for comparison in both family trees

[[Image:compare-detail.png]]
====Subtree Additional Information====

[[Image:Add info.JPG]]

To compare the subtrees in the overview section it is useful to have the possibility to add additional information to name and sex. The user can choose the attributes given in the box Additional Information.
It is possible to choose one or more categories. In this case, length of life, content, graduate and blood relation are chosen. For blood relation it is additionally necessary to define a name. After the name is chosen, in every subtree all people are marked with a pink point who have a blood relationship with this person. The attribute content shows just the average content because there is not enough space to display a bar. If a user wants to see this information in more detail, he has to use the option Member Detail.
With the given Information it is now possible to compare the two parts of the trees. For example, it seems to be that the members of the right subtree are more satisfied with there life than the members of the left subtree. To get a quick overview some attributes are summarized for every subtree in an additional box (not all attributes are displayed because date of birth or date of death can not be summarized in a meaningful way). The attribute important events would be displayed in this box as a list of all important events of all members ordered by date.
If I want to use these options to answer the question to study or not, I can see that the subtree with more graduated members seems to have a more “happy” life. Maybe they have also more successful important events? Then I would add the important event attribute in the overview section or use the Member Detail option…

====Member Detail====
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.

The simple data are written out right to their labels.

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.

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.

[[Image:member-detail.png]]

==References==
[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

------------------------------

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]

*[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]

File:Add info.JPG

2010-01-06T17:00:47Z

UE-InfoVis0910 0251293: New page: == Summary == == Copyright status == == Source ==

== Summary ==

== Copyright status ==

== Source ==

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 2

2009-11-20T19:01:00Z

UE-InfoVis0910 0251293:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]
=== Original table ===
[[Image:expenditure-categ.JPG]]

=== Critic on original table ===

Even the table seems to be structured it is difficult to compare the data. The unsteady intervals between the horizontal and vertical lines make it difficult to group the data intuitive. It is hardly possible to track the data accross the table without confusing lines
and columns. Furthermore the vertical rule divides the numbers just vertically which draws the attention to the vertical sections.

Beside that it is not clear at once which columns belong together or how they are grouped. It takes you a while to read and compare the headers and the text describing the row information. Especially the summaries at the right side and the end of the table should be highlighted in
some way.

Another weak point of this table is the differing alignment and the
maybe unfamiliar format of the numbers.

Missing unit in expenditure columns.

=== Redesigned table ===
[[Image:expenditure-categ-repaired-2.png]]

=== Changes applied to table ===

Second row, the one with ordinal numerals had no meaningful function. Because of that we decided to remove it completely from the table.

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.

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.

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.

Another change we made is addition of "Education type" into header row and removing of word "Education" 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.

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. This has also the positve effect that it is now more easier to
identify the different types of the presented data(% and amount of money). Between the rows and columns it is not necessary to include any additional seperators due to the steady interval and the right choice of space. This has the advantage that no more components have to be used which would maybe draw the attention away from the more important numbers. Reader can now easily compare expenditures for each type of education and find the results for each row and each column.

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]

*[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 2

2009-11-20T18:19:26Z

UE-InfoVis0910 0251293:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]
=== Original table ===
[[Image:expenditure-categ.JPG]]

=== Critic on original table ===

Even the table seems to be structured it is difficult to compare the data. The unsteady intervals between the horizontal and vertical lines make it difficult to group the data intuitive. It is hardly possible to track the data accross the table without confusing lines
and columns. Furthermore the vertical rule divides the numbers just vertically which draws the attention to the vertical sections.

Beside that it is not clear at once which columns belong together or how they are grouped. It takes you a while to read and compare the headers and the text describing the row information.

Another weak point of this table is the differing alignment and the
maybe unfamiliar format of the numbers.

Missing unit in expenditure columns.

=== Redesigned table ===
[[Image:expenditure-categ-repaired-2.png]]

=== Changes applied to table ===

Second row, the one with ordinal numerals had no meaningful function. Because of that we decided to remove it completely from the table.

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.

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.

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.

Another change we made is addition of "Education type" into header row and removing of word "Education" 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.

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. This has also the positve effect that it is now more easier to
group the different types of the presented data(% and numbers) Between the horizontally lines it is not necessary to include any additional seperators due to the steady interval and the right choice of space. This has the advantage that no more components have to be used which would maybe draw the attention away from the more important figures. Reader can now easily compare expenditures for each type of education and find the results for each row and each column.

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]

*[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 2

2009-11-20T16:30:47Z

UE-InfoVis0910 0251293:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]
=== Original table ===
[[Image:expenditure-categ.JPG]]

=== Critic on original table ===

Even the table seems to be structured it is difficult to compare the data. The vertical lines and the unsteady intervals between the horizontal lines make it difficult to group the data intuitive.

Missing unit in expenditure columns.

=== Redesigned table ===
[[Image:expenditure-categ-repaired-2.png]]

=== Changes applied to table ===

Second row, the one with ordinal numerals had no meaningful function. Because of that we decided to remove it completely from the table.

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.

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.

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.

Another change we made is addition of "Education type" into header row and removing of word "Education" 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.

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.

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2009/10|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/ UE InfoVis]

*[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13]]

Talk:Golden Ratio

2009-11-06T21:46:26Z

UE-InfoVis0910 0251293:

=Überarbeitung des Artikels im Zuge der InfoVis-Übung=

==Bilder==
Die aktuellen Bilder (von Vorgänger) sind nicht referenziert. Ich kann sie gerne herausnehmen wenn gewünscht. Bitte ein kurzes Kommentar dazu.

==DEFINITION==
* Im ersten Satz wurden einige alternative Begriffe für den goldenen Schnitt (in einem Satz) aufgezählt. Aus Gründen der Übersichtlichkeit habe ich das nach hinten die Definition verschoben.
* Einleitung strukturell gänzlich abgeändert
* Eineige sprachliche Änderungen
* Änderungen an dem geschichtlichen Teil, da Pythagoras nicht als "Entdecker" - eher "Forcierer" - des goldenen Schnitts angegeben werden kann. Ansonst habe ich den geschichtlichen Teil nicht verlängert, weil ich es gut finde, dass der Erstautor, das nur am Rande angeschnitten hat. Ausführlicheres darüber kann ja ruhig Bei Wikipedia nachgelesen werden.

== Andere Unterkapitel ==
* Die reine kurze Aufzählung von Beispielen, in denen der goldene Schnitt vorkommt, halte ich für gut. Hier habe ich nur einige sprachliche Änderungen vorgenommen.
* Fibonacci-Teil etwas mehr geändert

-- [[User:UE-InfoVis091_0427422|UE-InfoVis091_0427422]]

==Referenzierungen==

Einige Referenzierungen waren zu korrigieren bzw. zu löschen (redundant). Ein Link hat nicht funktioniert, ich wusste
nicht wie ich den Ursprung der Information hätte finden sollen.
[Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html

Ich habe in google und auf Online Bibliotheken gesucht aber nichts gefunden.

File:Golden rectangle.png

2009-11-06T21:43:27Z

UE-InfoVis0910 0251293:

== Summary ==

== Copyright status ==

== Source ==

[Wikipedia, 2009b] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle

File:Pentagram2.png

2009-11-06T21:42:42Z

UE-InfoVis0910 0251293:

== Summary ==

== Copyright status ==

== Source ==

[Wikipedia, 2005c] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

Golden Ratio

2009-11-06T21:41:53Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, 2009a]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]

The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean'''[Joyce, 1997]:

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, 2009a] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:cards.jpg|120px]]
|- align=center
| 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.|| if you measure a credit-card, the outcome would be a perfect golden rectangle.
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| The Great Pyramid has proportions designed according to golden ratio.[Obara, 2000]|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.[Obara, 2000]|| 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.[Knott, 2009]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] David E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Obara, 2000] Samuel Obara. Golden Ratio in Art and Architectue. The University of Georgia. Retrieved at: November 6, 2009. http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[Knott, 2009] Ron Knott. Fibonacci Numbers and The Golden Section in Art, Architecture and Music. Retrieved at: November 6, 2009. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html

[Wikipedia, 2009a] Wikipedia.org, Golden Ratio, Created at: October 19, 2005. Retrieved at: November 6, 2009. http://en.wikipedia.org/wiki/Golden_ratio

[Wikipedia, 2009b] Wikipedia.org, Golden rectangle, Created at: Ocotober 24, 2005, Retrieved at: November 6, 2009. http://en.wikipedia.org/wiki/Golden_rectangle

[Wikipedia, 2009c] Wikipedia.org, Pentagram, Created at: 29 October, 2005, Retrieved at: November 6, 2009. http://en.wikipedia.org/wiki/Pentagram
[[Category:Glossary]]

Golden Ratio

2009-11-06T21:38:39Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]

The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean'''[Joyce, 1997]:

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:cards.jpg|120px]]
|- align=center
| 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.|| if you measure a credit-card, the outcome would be a perfect golden rectangle.
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| The Great Pyramid has proportions designed according to golden ratio.[Obara, 2000]|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.[Obara, 2000]|| 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.[Knott, 2009]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] David E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Obara, 2000] Samuel Obara. Golden Ratio in Art and Architectue. The University of Georgia. Retrieved at: November 6, 2009. http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[Knott, 2009] Ron Knott. Fibonacci Numbers and The Golden Section in Art, Architecture and Music. Retrieved at: November 6, 2009. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html

[Wikipedia, 2005a] Wikipedia.org, Golden Ratio, Created at: October 19, 2005. Retrieved at: November 6, 2009. http://en.wikipedia.org/wiki/Golden_ratio

[Wikipedia, 2005b] Wikipedia.org, Golden rectangle, Created at: Ocotober 24, 2005, Retrieved at: November 6, 2009. http://en.wikipedia.org/wiki/Golden_rectangle

[Wikipedia, 2005c] Wikipedia.org, Pentagram, Created at: 29 October, 2005, Retrieved at: November 6, 2009. http://en.wikipedia.org/wiki/Pentagram
[[Category:Glossary]]

Golden Ratio

2009-11-06T21:31:06Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]

The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean'''[Joyce, 1997]:

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:cards.jpg|120px]]
|- align=center
| 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.|| if you measure a credit-card, the outcome would be a perfect golden rectangle.
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| The Great Pyramid has proportions designed according to golden ratio.[Obara, 2000]|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.[Obara, 2000]|| 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.[Knott, 2009]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] David E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Obara, 2000] Samuel Obara. Golden Ratio in Art and Architectue. The University of Georgia. Retrieved at: November 6, 2009. http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[Knott, 2009] Ron Knott. Fibonacci Numbers and The Golden Section in Art, Architecture and Music. Retrieved at: November 6, 2009. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html

[[Category:Glossary]]

File:Polyplaza.jpg

2009-11-06T20:57:19Z

UE-InfoVis0910 0251293:

== Summary ==

== Copyright status ==

== Source ==

[Knott, 2009] Ron Knott. Fibonacci Numbers and The Golden Section in Art, Architecture and Music. Retrieved at: November 6, 2009. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html

File:Great-pyramid.gif

2009-11-06T20:56:44Z

UE-InfoVis0910 0251293:

== Summary ==

== Copyright status ==

== Source ==

[Obara, 2000] Samuel Obara. Golden Ratio in Art and Architectue. The University of Georgia. Retrieved at: November 6, 2009. http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

Golden Ratio

2009-11-06T20:56:04Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]
[Joyce, 1997]
The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:cards.jpg|120px]]
|- align=center
| 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.|| if you measure a credit-card, the outcome would be a perfect golden rectangle.
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| The Great Pyramid has proportions designed according to golden ratio.[Obara, 2000]|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.[Obara, 2000]|| 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.[Knott, 2009]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] David E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Obara, 2000] Samuel Obara. Golden Ratio in Art and Architectue. The University of Georgia. Retrieved at: November 6, 2009. http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[Knott, 2009] Ron Knott. Fibonacci Numbers and The Golden Section in Art, Architecture and Music. Retrieved at: November 6, 2009. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html

[[Category:Glossary]]

File:Pentagram2.png

2009-11-06T20:48:05Z

UE-InfoVis0910 0251293:

== Summary ==

== Copyright status ==

== Source ==

[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

File:Golden rectangle.png

2009-11-06T20:46:34Z

UE-InfoVis0910 0251293:

== Summary ==

== Copyright status ==

== Source ==

[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle

File:Golden-ratio-graphical.png

2009-11-06T20:45:12Z

UE-InfoVis0910 0251293:

== Summary ==

== Copyright status ==

== Source ==

[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio

Visual Clutter

2009-11-06T20:42:25Z

UE-InfoVis0910 0251293:

== Definition ==

{{Quotation|Clutter is the state in which excess items, or their representation or organization, lead to a degradation of performance at some task. |[Rosenholtz et al., 2005]}}

* Clutter may refer to any of the following:
** A confusing or disorderly state or collection; or the creation thereof. Excessive, unnecessary or uncontrolled clutter in a home or office is a sign of compulsive hoarding.
** Cluttering, a communication disorder
** The Clutter family, whose murder was documented in the Truman Capote "nonfiction novel" In Cold Blood
** A type of light pollution
** Unwanted echoes in electronic systems, particularly in refference to radars. Such echoes are typically returned from ground, sea, rain, animals, chaff and atmospheric turbulences.
** The jumble of odd posts placed in the first Top Level Post of a User Friendly member's diary by the Cluttersquad [http://en.wikipedia.org/wiki/Clutter ''http://en.wikipedia.org/wiki/Clutter'']

== Introduction ==

Clutter is an important phenomenon in our lives, and an important consideration in the design of user interfaces and information visualizations. Many existing visualization systems are designed to reduce clutter by filtering what objects or information the user sees, or using non-linear magnification techniques so that objects in the center of the screen are allowed more display area. Tips for designing web pages, maps, and other visualizations often focus on techniques for displaying a large amount of information while keeping clutter to a minimum through careful choices of representation and organization of that information. [Rosenholtz et al., 2005]

== Web pages ==

A home page might contain a logo and tag line, an attractive graphic, some site navigation buttons, and a welcome message. Now, it's common to see all of that and much more, including:

* Headlines and text for multiple news items
* Separate headers and quick links for several site features
* An assortment of graphics for promotions and advertisements
* Logos for various affiliates, memberships, and awards
* Copyright notices and other legal disclaimers [Meadhra, 2004]

An example for this is the first page of GMX.at. This page is full of commercials and news headlines. One popular service of GMX is its webmail service. The login form is surrounded by visual clutter and it is easy to be overlooked.

[[Image:0225061_01_Screen3.jpg|thumb|200px|none|GMX.at start page]]

== Geological Maps ==

Visual Clutter in the Topographic Base of Geological Maps

Geological maps are arguably the most complicated visual displays in common use and so they were a good subject for an experiment to understand the nature of visual clutter. But this experiment also tackles the practical problem of how best to simplify the topographic base on geological maps.

[[Image:Erste.png]]

[[Image:zweite1.png]] [[Image:dritte1.png]][[Image:vierte1.png]][[Image:fünfte1.png]]
[[Image:sechs1.png]]

Here is a small detail from one of the test maps used in the experiments and examples of the five types of topographic base which were compared: 'full', 'line', 'point', 'minimal' and 'design'. These bases were printed in grey and geological information was superimposed. The experiment compared the relative importance of line symbols and point symbols in causing visual clutter, but account was also taken of the importance placed on different topographic symbols by professional map users.

Abstract - Visual clutter on maps is a familiar experience but its precise nature is only poorly understood. Clutter was investigated in an experiment using a 1:50 000 geological map. Twelve representative map reading tasks were used to compare map reading performance on maps which differed only in their topographic base. The aim was to assess the effect of removing topographic symbols which are of only minor importance to the map reader. This reduction in visual clutter significantly improved performance on a number of the questions. Some evidence was obtained to support the hypothesis that line symbols clutter other line symbols, and point symbols clutter other point symbols, but there is little effect between the two. In practical terms the removal of minor point symbols and type led to larger improvements than the removal of minor line symbols, even though more of the latter were deleted. The relevance of the experiment to other geological maps, and to maps in general, is discussed. [Phillips, 1982]

== Bibliography ==

:[Rosenholtz et al., 2005] Ruth Rosenholtz, Yuanzhen Li, Jonathan Mansfield, and Zhenlan Jin. Feature Congestion: A Measure of Display Clutter. Retrieved at: Nov 24, 2009. http://web.mit.edu/rruth/www/Papers/RosenholtzEtAlCHI2005Clutter.pdf

:[Meadhra, 2004] Michael Meadhra, Reduce visual clutter to improve usability. Created at: May 20, 2004. Retrieved at: Oct 24, 2005. http://www.builderau.com.au/program/web/0,39024632,39129000,00.htm

:[Phillips, 1982] Richard J. Phillips. An Investigation of Visual Clutter in the Topographic Base of a Geological Map. ''The Cartographic Journal'', Vol.19, No.2: 122-132, December 1982. http://richardphillips.org.uk/maps/symbols.html#ge

[[Category:Glossary]]

Visual Clutter

2009-11-06T20:41:45Z

UE-InfoVis0910 0251293:

== Definition ==

{{Quotation|Clutter is the state in which excess items, or their representation or organization, lead to a degradation of performance at some task. |[Rosenholtz et al., 2005]}}

* Clutter may refer to any of the following:
** A confusing or disorderly state or collection; or the creation thereof. Excessive, unnecessary or uncontrolled clutter in a home or office is a sign of compulsive hoarding.
** Cluttering, a communication disorder
** The Clutter family, whose murder was documented in the Truman Capote "nonfiction novel" In Cold Blood
** A type of light pollution
** Unwanted echoes in electronic systems, particularly in refference to radars. Such echoes are typically returned from ground, sea, rain, animals, chaff and atmospheric turbulences.
** The jumble of odd posts placed in the first Top Level Post of a User Friendly member's diary by the Cluttersquad [http://en.wikipedia.org/wiki/Clutter ''http://en.wikipedia.org/wiki/Clutter'']

== Introduction ==

Clutter is an important phenomenon in our lives, and an important consideration in the design of user interfaces and information visualizations. Many existing visualization systems are designed to reduce clutter by filtering what objects or information the user sees, or using non-linear magnification techniques so that objects in the center of the screen are allowed more display area. Tips for designing web pages, maps, and other visualizations often focus on techniques for displaying a large amount of information while keeping clutter to a minimum through careful choices of representation and organization of that information. [Rosenholtz et al., 2005]

== Web pages ==

A home page might contain a logo and tag line, an attractive graphic, some site navigation buttons, and a welcome message. Now, it's common to see all of that and much more, including:

* Headlines and text for multiple news items
* Separate headers and quick links for several site features
* An assortment of graphics for promotions and advertisements
* Logos for various affiliates, memberships, and awards
* Copyright notices and other legal disclaimers [Meadhra, 2004]

An example for this is the first page of GMX.at. This page is full of commercials and news headlines. One popular service of GMX is its webmail service. The login form is surrounded by visual clutter and it is easy to be overlooked.

[[Image:0225061_01_Screen3.jpg|thumb|200px|none|GMX.at start page]]

== Geological Maps ==

Visual Clutter in the Topographic Base of Geological Maps

Geological maps are arguably the most complicated visual displays in common use and so they were a good subject for an experiment to understand the nature of visual clutter. But this experiment also tackles the practical problem of how best to simplify the topographic base on geological maps.

[[Image:Erste.png]]

[[Image:zweite1.png]] [[Image:dritte1.png]][[Image:vierte1.png]][[Image:fünfte1.png]]
[[Image:sechs1.png]]

Here is a small detail from one of the test maps used in the experiments and examples of the five types of topographic base which were compared: 'full', 'line', 'point', 'minimal' and 'design'. These bases were printed in grey and geological information was superimposed. The experiment compared the relative importance of line symbols and point symbols in causing visual clutter, but account was also taken of the importance placed on different topographic symbols by professional map users.

Abstract - Visual clutter on maps is a familiar experience but its precise nature is only poorly understood. Clutter was investigated in an experiment using a 1:50 000 geological map. Twelve representative map reading tasks were used to compare map reading performance on maps which differed only in their topographic base. The aim was to assess the effect of removing topographic symbols which are of only minor importance to the map reader. This reduction in visual clutter significantly improved performance on a number of the questions. Some evidence was obtained to support the hypothesis that line symbols clutter other line symbols, and point symbols clutter other point symbols, but there is little effect between the two. In practical terms the removal of minor point symbols and type led to larger improvements than the removal of minor line symbols, even though more of the latter were deleted. The relevance of the experiment to other geological maps, and to maps in general, is discussed. [Phillips, 1982]

== Bibliography ==

:[Rosenholtz et al., 2005] Ruth Rosenholtz, Yuanzhen Li, Jonathan Mansfield, and Zhenlan Jin. Feature Congestion: A Measure of Display Clutter.Retrieved at: Nov 24, 2009.http://web.mit.edu/rruth/www/Papers/RosenholtzEtAlCHI2005Clutter.pdf

:[Meadhra, 2004] Michael Meadhra, Reduce visual clutter to improve usability. Created at: May 20, 2004. Retrieved at: Oct 24, 2005. http://www.builderau.com.au/program/web/0,39024632,39129000,00.htm

:[Phillips, 1982] Richard J. Phillips. An Investigation of Visual Clutter in the Topographic Base of a Geological Map. ''The Cartographic Journal'', Vol.19, No.2: 122-132, December 1982. http://richardphillips.org.uk/maps/symbols.html#ge

[[Category:Glossary]]

Talk:Golden Ratio

2009-11-06T20:25:22Z

UE-InfoVis0910 0251293:

Golden Ratio

2009-11-06T20:22:14Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]
[Joyce, 1997]
The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:cards.jpg|120px]]
|- align=center
| 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.|| if you measure a credit-card, the outcome would be a perfect golden rectangle.
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| The Great Pyramid has proportions designed according to golden ratio.[Obara, 2000]|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.[Obara, 2000]|| 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.[Knott, 2009]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] David E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Obara, 2000] Samuel Obara. Golden Ratio in Art and Architectue. The University of Georgia. Retrieved at: November 6, 2009.''[http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html]''

[Knott, 2009] Ron Knott. Fibonacci Numbers and The Golden Section in Art, Architecture and Music. Retrieved at: November 6, 2009.''[http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html]''

[[Category:Glossary]]

Golden Ratio

2009-11-06T20:18:18Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]
[Joyce, 1997]
The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:cards.jpg|120px]]
|- align=center
| 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.
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| The Great Pyramid has proportions designed according to golden ratio.[Obara, 2000]|| Even in proportions of Parthenon you can find golden spiral consisting of golden rectangles.[Obara, 2000]|| 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.[Knott, 2009]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] David E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Obara, 2000] Samuel Obara. Golden Ratio in Art and Architectue. The University of Georgia. Retrieved at: November 6, 2009.''[http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html]''

[Knott, 2009] Ron Knott. Fibonacci Numbers and The Golden Section in Art, Architecture and Music. Retrieved at: November 6, 2009.''[http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html]''

[[Category:Glossary]]

Golden Ratio

2009-11-06T20:14:48Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]
[Joyce, 1997]
The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:cards.jpg|120px]]
|- align=center
| 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]
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| 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]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] Davic E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Obara, 2000] Samuel Obara. Golden Ratio in Art and Architectue. The University of Georgia. Retrieved at: November 6, 2009.''[http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html]''

[Knott, 2009] Ron Knott. Fibonacci Numbers and The Golden Section in Art, Architecture and Music. Retrieved at: November 6, 2009.''[http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html]''

[[Category:Glossary]]

File:Cards.jpg

2009-11-06T20:13:10Z

UE-InfoVis0910 0251293:

== Summary ==

== Copyright status ==

Diese Datei wurde unter der GNU-Lizenz für freie Dokumentation veröffentlicht.

Es ist erlaubt, die Datei unter den Bedingungen der GNU-Lizenz für freie Dokumentation, Version 1.2 oder einer späteren Version, veröffentlicht von der Free Software Foundation, zu kopieren, zu verbreiten und/oder zu modifizieren. Es gibt keine unveränderlichen Abschnitte, keinen vorderen Umschlagtext und keinen hinteren Umschlagtext.
== Source ==

''[http://www.sxc.hu/browse.phtml?f=view&id=206578]''

Golden Ratio

2009-11-06T20:07:59Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]
[Joyce, 1997]
The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:cards.jpg|120px]]
|- align=center
| 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]
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| 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]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] Davic E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html

[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

[Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images

[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

[Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/

[Samuel Obara]http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[[Category:Glossary]]

File:Cards.jpg

2009-11-06T20:04:27Z

UE-InfoVis0910 0251293: New page: == Summary == == Copyright status == == Source ==

== Summary ==

== Copyright status ==

== Source ==

Golden Ratio

2009-11-06T19:37:22Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]
[Joyce, 1997]
The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:card.jpg|120px]]
|- align=center
| 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]
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| 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]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] Davic E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html

[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

[Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images

[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

[Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/

[Samuel Obara]http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[[Category:Glossary]]

Golden Ratio

2009-11-06T19:34:54Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]

The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:card.jpg|120px]]
|- align=center
| 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]
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| 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]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Joyce, 1997] Davic E.Joyce. Euclid Elements Book 6, Definition 3. Retrieved at: November 6, 2009.''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]''

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html

[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

[Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images

[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

[Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/

[Samuel Obara]http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[[Category:Glossary]]

Golden Ratio

2009-11-06T19:26:02Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.[Livio, 2002]

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Summerson, 1963]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]

The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:card.jpg|120px]]
|- align=center
| 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]
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| 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]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson, 1963] John Summerson. Heavenly Mansions: And Other Essays on Architecture. Norton, New York, 1963, p.37

[Euclid-book6]Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html

[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

[Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images

[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

[Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/

[Samuel Obara]http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[[Category:Glossary]]

Golden Ratio

2009-11-06T19:11:42Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.

Other names used for the golden ratio are '''golden section''', '''golden mean''', '''extreme and mean ratio''', '''medial section''', '''golden proportion''', '''golden cut''' and '''golden number'''
[Livio, 2002]

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]

The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:card.jpg|120px]]
|- align=center
| 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]
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| 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]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[Livio, 2002] Mario Livio. The Golden Ratio: The Story of Phi, The World's most Astonishing Number. Broadway Books, New York, 2002

[Summerson John-1963-Heavenly Mansions]Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. "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."

[Euclid-book6]Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html

[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

[Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images

[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

[Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/

[Samuel Obara]http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[[Category:Glossary]]

Talk:Golden Ratio

2009-11-06T18:01:56Z

UE-InfoVis0910 0251293:

=Überarbeitung des Artikels im Zuge der InfoVis-Übung=

==Bilder==
Die aktuellen Bilder sind nicht referenziert. Ich kann sie gerne herausnehmen wenn gewünscht. Bitte ein kurzes Kommentar dazu.

==DEFINITION==
* Im ersten Satz wurden einige alternative Begriffe für den goldenen Schnitt (in einem Satz) aufgezählt. Aus Gründen der Übersichtlichkeit habe ich das zu einer Aufzählung geändert. Klarer Vorteil: Die Definition ist nur noch ein kurzer Satz und wird nicht mehr von einer reinen Aufzählung unterbrochen. Ich habe die Aufzählung dennoch direkt hinter der textuellen Definition (und somit vor der formalen) plaziert, damit LeserInnen, die nach anderen Termini suchen, diese sofort im Auge haben. Die Begriffsaufzählung dieser Art ist möglicherweise (zumindest bei Wikipedia) eher ungewöhnlich. Wenn das auf keinen Anklang findet, kann man es gerne wieder umändern.
* Die mathematische Definition ist nur ein Teil des goldenen Schnittes. Deshalb sollt auch die Information über die Verwendung und Bedeutung des Goldenen Schnitts bei der ersten mathematischen Definition stehen, um den Leser möglichst schnell ein erstes möglichst vollständiges Bild des Begriffs zu vermitteln.
* Einleitung strukturell gänzlich abgeändert
* Eineige sprachliche Änderungen
* Änderungen an dem geschichtlichen Teil, da Pythagoras nicht als "Entdecker" - eher "Forcierer" - des goldenen Schnitts angegeben werden kann. Ansonst habe ich den geschichtlichen Teil nicht verlängert, weil ich es gut finde, dass der Erstautor, das nur am Rande angeschnitten hat. Ausführlicheres darüber kann ja ruhig Bei Wikipedia nachgelesen werden.

== Andere Unterkapitel ==
* Die reine kurze Aufzählung von Beispielen, in denen der goldene Schnitt vorkommt, halte ich für gut. Hier habe ich nur einige sprachliche Änderungen vorgenommen.
* Fibonacci-Teil etwas mehr geändert

Talk:Golden Ratio

2009-11-06T18:00:45Z

UE-InfoVis0910 0251293:

=Überarbeitung des Artikels im Zuge der InfoVis-Übung=

==Bilder==
Die aktuellen Bilder sind nicht referenziert. Ich kann sie gerne herausnehmen wenn gewünscht. Bitte ein kurzes Kommentar dazu.

==DEFINITION==
* Im ersten Satz wurden einige alternative Begriffe für den goldenen Schnitt (in einem Satz) aufgezählt. Aus Gründen der Übersichtlichkeit habe ich das zu einer Aufzählung geändert. Klarer Vorteil: Die Definition ist nur noch ein kurzer Satz und wird nicht mehr von einer reinen Aufzählung unterbrochen. Ich habe die Aufzählung dennoch direkt hinter der textuellen Definition (und somit vor der formalen) plaziert, damit LeserInnen, die nach anderen Termini suchen, diese sofort im Auge haben. Die Begriffsaufzählung dieser Art ist möglicherweise (zumindest bei Wikipedia) eher ungewöhnlich. Wenn das auf keinen Anklang findet, kann man es gerne wieder umändern.
*Die mathematische Definition ist nur ein Teil des goldenen Schnittes. Deshalb sollt auch die Information über die Verwendung
und Bedeutung des Goldenen Schnitts bei der ersten mathematischen Definition stehen, um den Leser möglichst schnell ein erstes möglichst vollständiges Bild des Begriffs zu vermitteln.

* Einleitung strukturell gänzlich abgeändert
* Eineige sprachliche Änderungen
* Änderungen an dem geschichtlichen Teil, da Pythagoras nicht als "Entdecker" - eher "Forcierer" - des goldenen Schnitts angegeben werden kann. Ansonst habe ich den geschichtlichen Teil nicht verlängert, weil ich es gut finde, dass der Erstautor, das nur am Rande angeschnitten hat. Ausführlicheres darüber kann ja ruhig Bei Wikipedia nachgelesen werden.

== Andere Unterkapitel ==
* Die reine kurze Aufzählung von Beispielen, in denen der goldene Schnitt vorkommt, halte ich für gut. Hier habe ich nur einige sprachliche Änderungen vorgenommen.
* Fibonacci-Teil etwas mehr geändert

Golden Ratio

2009-11-06T17:52:35Z

UE-InfoVis0910 0251293:

== GOLDEN RATIO ==

----
===DEFINITION===
The '''golden ratio''' is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. [Wikipedia, Golden Ratio, 2009]

This mathematical proportion is often recognized as 'aesthetically pleasing', thus it is often found in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.

Other names used for the golden ratio are:
* '''golden section'''
* '''golden mean'''
* '''extreme and mean ratio'''
* '''medial section'''
* '''golden proportion'''
* '''golden cut'''
* '''golden number'''

It is said, that two quantities are in golden ration if and only if the following condition holds:

[[Image:golden-ratio.png]]

It is mostly symbolised by the Greek letter [[Image:Phi.png]] (phi) or sometimes by the less known τ (tau).

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]

The history of the golden ration at least goes back to the ancient greeks, Pythagoras and his followers. The greek mathematician Euclid of Alexandria (365BC - 300BC) first mentioned the '''golden mean''':

{{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)}}

----

===CALCULATION===

Method for calculation of golden ratio constant is beginning from the following algebraic formula:

[[Image:golden-ratio.png]]

From the formula we obtain that a is equal b/[[Image:Phi.png]], so we can replace all occurences of a:

[[Image:golden-ratio-1.png]]

Devided by b formula changes to:

[[Image:golden-ratio-2.png]]

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:

[[Image:golden-ratio-3.png]]

The only positive result to above equation is the irrational number we have already presented:

[[Image:golden-ratio-4.png]]

----

===GEOMETRY AND MATHEMATICS===

Fibonacci introduced a sequence of numbers, today called the '''Fibonacci Numbers''', which is often found in natural sciences. By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two [Wikipedia, Golden Ratio, 2009] .

1,2,3,5,8,13,21,34,55,89,144,233,377,....

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:

[[Image:fibonacci-example-1.png]]

and by smaller devided by bigger number:

[[Image:fibonacci-example-2.png]]

There are many shapes in which golden ratio were discovered. Examples of those you can see on the right side.

{| cellpadding="1" style="border:1px solid darkgray;"
!width="140"|Pentagram
!width="150"|Golden rectangle
|- align=center
| style="border:1px solid;"|
[[Image:Pentagram2.png|120px]]
| style="border:1px solid;"|
[[Image:Golden_rectangle.png|120px]]
|- align=center
|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.
|}

----

===ART & DESIGN===

Since the beginning of ART & 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.
{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Mona-Liza
!width="150"|Aztek decorations
!width="130"|Credit cards
|- align=center
| style="border:1px solid;"|
[[Image:mona-liza.gif]]
| style="border:1px solid;"|
[[Image:aztec.jpg|120px]]
| style="border:1px solid;"|
[[Image:card.jpg|120px]]
|- align=center
| 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]
|}

----

===Architecture===

There is many examples of golden ratio even in architecture. Architect were inspired by this "sacred ratio" already in times of Pyramids. Even in Greek you can find golden rectangles, spirals, etc. In the table below you can find several examples.

{| cellpadding="2" style="border:1px solid darkgray;"
!width="140"|Great Pyramid of Giza
!width="150"|Parthenon
!width="130"|Engineering Plaza
|- align=center
| style="border:1px solid;"|
[[Image:great-pyramid.gif]]
| style="border:1px solid;"|
[[Image:parthenon.gif|120px]]
| style="border:1px solid;"|
[[Image:polyplaza.jpg|120px]]
|- align=center
| 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]
|}

----

== Related Links ==
*[http://www.goldenmeangauge.co.uk/fibonacci.htm The Fibonacci Series]
*[http://www.golden-section.eu Der goldene Schnitt - Das Mysterium der Schönheit]
[Wikipedia, Golden Ratio, 2005] Wikipedia.org, Golden Ratio, 19.10.2005, http://en.wikipedia.org/wiki/Golden_ratio
[Wikipedia, Golden rectangle, 2005] Wikipedia.org, Golden rectangle, 24.10.2005, http://en.wikipedia.org/wiki/Golden_rectangle
[Wikipedia, Pentagram, 2005] Wikipedia.org, Pentagram, 29.10.2005, http://en.wikipedia.org/wiki/Pentagram

==REFERENCES==

[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}}

[Summerson John-1963-Heavenly Mansions]Summerson John, ''Heavenly Mansions: And Other Essays on Architecture'' (New York: W.W. Norton, 1963) p. 37. "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."

[Euclid-book6]Euclid, ''[http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Elements]'', Book 6, Definition 3.

[Kaphammel, 2000] Günther Kahammel, Der goldene Schnitt, 1. Auflage, Braunschweig, 2000

[Brooker] Carolyn Brooker, The Golden Ratio in the Arts, University of Bath, http://students.bath.ac.uk/ma1caab/art.html

[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

[Batterywholesaler] Batterywholesaler, Credit Cards, http://www.batterywholesaler.co.uk/battery_images

[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

[Livio, 2002] Mario Livio, The golden ratio and aesthetics, November 2002, http://plus.maths.org/issue22/features/golden/

[Samuel Obara]http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

[[Category:Glossary]]

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13

2009-10-21T21:32:43Z

UE-InfoVis0910 0251293:

== Gruppenmitglieder ==
[[User:UE-InfoVis0910_0827462|Sadauskas, Martin]] 
[[User:UE-InfoVis091_0427422|Scheikl, Daniel]] 
[[User:UE-InfoVis0910_0251293|Burger, Martin]]

== Aufgaben ==
[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 0|Aufgabe 0]] 
[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 1|Aufgabe 1]] 
[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 2|Aufgabe 2]] 
[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 3|Aufgabe 3]] 
[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 4|Aufgabe 4]]

Teaching:TUW - UE InfoVis WS 2009/10

2009-10-21T21:31:27Z

UE-InfoVis0910 0251293:

[[Image:Aigner03infovis ue.gif]] <big>WS 2009/10</big>

'''LVA Nr:''' 188.308 ([http://tuwis.tuwien.ac.at/lva/tuwien/188308 TUWIS++ Seite])

'''LVA Homepage:''' http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/index.html

'''Leitung:''' [[Gschwandtner, Theresia|Theresia Gschwandtner]] [gschwandtner (at) ifs.tuwien.ac.at] 

== Gruppen ==


[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 02|Gruppe 02 (Feichtinger, Rezaei, Schindelka)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 03|Gruppe 03 (Lang, Hackl, Hasslacher)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 04|Gruppe 04 (Kaiser, <NACHNAME>, Ehsani)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 05|Gruppe 05 (Paizoni, Wuttej, Hudl)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 06|Gruppe 06 (Fried, Fritz, Hiller)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 07|Gruppe 07 (Schwengerer, <???>, <???>)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 09|Gruppe 09 (Hubmann-Haidvogel, Kloibhofer, Riederer)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13 (Sadauskas, Scheikl, Burger)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 14|Gruppe 14 (Gastecker, Hahn, Leeb)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 15|Gruppe 15 (Martin, Stix, Lenzhofer)]]

== News / Bemerkungen ==

Liebe TeilnehmerInnen! 
Um diese Seite einheitlich zu gestalten (auch bezüglich der Vorjahre), schlage ich vor die Nachnamen
der Gruppenmitglieder in Klammer neben der Gruppe anzugeben, 
z.B.: Gruppe XX (Maier, Müller, Mustermann). 
-- [[Gschwandtner, Theresia|Theresia Gschwandtner]] 10:05, 01 October 2009 (CEST)

User:UE-InfoVis0910 0251293

2009-10-21T21:26:48Z

UE-InfoVis0910 0251293:

== Martin Burger ==

[[{{ns:6}}:burger_martin_pic02.jpg]]

===Basic Personal Data===

* '''Name:''' Martin Burger
* '''Registration Number:''' 0251293
* '''E-mail:''' h0251293@wu-wien.ac.at
* '''Field:''' Information- and Knowledgemanagement
===General===

* [http://en.wikipedia.org/ Wikipedia].
* most recent amendment: [[User:UE-InfoVis0910 0251293|UE-InfoVis0910 0251293]] 23:06, 21 October 2009 (CEST)

User:UE-InfoVis0910 0251293

2009-10-21T21:06:26Z

UE-InfoVis0910 0251293:

== Martin Burger ==

[[{{ns:6}}:burger_martin_pic02.jpg]]

===Persönliches===

Hallo,

mein Name ist Martin Burger und bin erst seit kurzem an der TU.
Hauptsächlich arbeite ich bei REWE International, wo ich es des öfteren
mit Datenanalysen und Präsentationen zu tun habe. Deshalb auch die
Entscheidung diesen Kurs zu besuchen.

===Allgemein===

* [http://en.wikipedia.org/ Wikipedia].
* letzte Änderung [[User:UE-InfoVis0910 0251293|UE-InfoVis0910 0251293]] 23:06, 21 October 2009 (CEST)

User:UE-InfoVis0910 0251293

2009-10-21T20:29:07Z

UE-InfoVis0910 0251293:

[[{{ns:6}}:burger_martin_pic02.jpg]]

Martin
Burger

File:Burger martin pic02.jpg

2009-10-21T20:27:14Z

UE-InfoVis0910 0251293: New page: == Summary == == Copyright status == == Source ==

== Summary ==

== Copyright status ==

== Source ==

File:Martin burger pic.jpg

2009-10-21T20:16:39Z

UE-InfoVis0910 0251293: New page: == Summary == == Copyright status == == Source ==

== Summary ==

== Copyright status ==

== Source ==

User:UE-InfoVis0910 0251293

2009-10-21T19:57:46Z

UE-InfoVis0910 0251293: New page: Martin Burger

Martin
Burger