InfoVis:Wiki - User contributions [en]

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 3

2009-12-03T08:02:55Z

UE-InfoVis091 0427422:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws09/infovis_ue_aufgabe3.html Beschreibung der Aufgabe 3]
=== Zu verbessernde Grafik ===
------------------------------- 
[[Image:nyt.gif]]

== Ausarbeitung ==

===Critics===
------------------------------- 

* If you are not familiar with those kinds of diagrams, they are a little hard to read at a first glance. It took me a few minutes until I understood, that "Total" is a company. Therefore the graphic made no sense at first. Of course, if you have the graphics embedded in an article this confusion would not happen at all. But still, if you have to study a graphics in a news paper (and not a scientific paper) for one or two minutes, just to understand it, you may just skip it. So in the context of a simple news paper this diagram may be a little to complicated.

* The y-axes shows the growth rate of the companies. This is quite easy to understand. What could be a little irritating are the circles that represent the total production of the year. At a first glance it looks like the circles are related to values of the y-axes, but they are absolutely not (only the center of the circle is relevant). The size of the circle represents information which is absolutely independent from the y-axes.

* The size of the circles and the growth rate (location on the y-axes and numbered value) alone don't really give you a hint, how the amount of production was in 2002. You can only use the size of the circles to compare this year's production of every company with all other. But wouldn't it also be interesting if you were able to compare the oil production for each company with its own production from 2002? Of course, the growth rate gives you exactly this information, but not in an eye-catching way. It would be, if you had a second circle for each company in the background (with the same center) in another color. Now we would have the size of the circles, that shows you the production amount, the second circle in the back, that gives you an idea how the production amount of each company has changed and the position on the diagram which makes it easy to compare the growth rates of one company with all others. The advantage of this redundant information is the easier way of comparison - the disadvantage is that it maybe makes the diagram even harder to understand at first ('cause there is one more information layer).

*Beside the fact that the data presented is not easy to understand, it is not clear what information should be focused. The chart shows a comparison of the major oil producers with detailed written information about the situation of Total. This divides the chart logically and visually into two parts, which can confuse the message. I think in this case the most important information should be an overview of all oil producers, which then can be referenced in a text where the situation of Total is explained in more detail.

*Further, it may be criticized that the legends describing the circles are positioned on the right hand side and the numbers describing the percentage of growth are on the left. As most readers start to read from left to right, the focus is first on the percentage of growth. Then they go further on to check the names of the companies. But this is the wrong way, because the original question is about the companies and their growth and not about the growth. For this reason the reader lose time to get the information. In addition, the scale produces a lot of white space without information, as between ExxonMobil and Royal Dutch Shell.

===Redesigned Graph===
------------------------------- 

[[Image:improved_graph_oil_prod.jpg]]

===Description of improvements===
------------------------------- 

*The data which should be focused in the first visual layer is clearly in front, underlined by bigger letters (percentage of growth) and different colours (green bars). The supporting components are designed with different colours and smaller letters to draw not to much attention.

* In the new version of the chart the scale is completely deleted. Instead numbers inside the bars show the growth. This allows a much more compact and clear presentation of the data.

*As the sequence was defined by the scale, the companies are already in the right order. It also makes sense to use this order as group definition for the new data bar. The new data bar is now possible because the original circles are now replaced by bars, which are visually easier to compare.

* Now the chart intuitive communicates a clear message through a better presentation of the data, even less elements are used. For this the Data-Ink Ration improved a lot comparing the old version with the new version.

File:Improved graph oil prod.jpg

2009-12-03T08:00:27Z

UE-InfoVis091 0427422: Improved graphic for InfoVis exercise

== Summary ==
Improved graphic for InfoVis exercise
== Copyright status ==

== Source ==

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 3

2009-12-01T16:04:14Z

UE-InfoVis091 0427422:

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 3

2009-11-25T22:22:47Z

UE-InfoVis091 0427422:

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 3

2009-11-25T21:53:30Z

UE-InfoVis091 0427422:

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 3

2009-11-24T22:40:14Z

UE-InfoVis091 0427422:

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 3

2009-11-24T22:38:18Z

UE-InfoVis091 0427422:

Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13 - Aufgabe 3

2009-11-24T22:37:41Z

UE-InfoVis091 0427422:

Golden Ratio

2009-11-06T18:29:28Z

UE-InfoVis091 0427422: Major rivision for InfoVis exercise: Changes in the format and text.

== 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'''

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]]

Talk:Golden Ratio

2009-11-06T18:29:05Z

UE-InfoVis091 0427422:

=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]]

Talk:Golden Ratio

2009-11-06T18:12:46Z

UE-InfoVis091 0427422:

Talk:Golden Ratio

2009-11-06T18:09:44Z

UE-InfoVis091 0427422:

=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

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

Talk:Golden Ratio

2009-11-06T17:48:45Z

UE-InfoVis091 0427422:

=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.

* 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

2009-11-06T17:47:41Z

UE-InfoVis091 0427422:

== 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]

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|]]

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.

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]]

Golden Ratio

2009-11-06T17:28:00Z

UE-InfoVis091 0427422:

== 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]

Other names used for the golden ratio are:
* '''golden section''' (Latin: sectio aurea)
* '''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|]]

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.

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 to us, the Fibonacci-Numbers:

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]]

Golden Ratio

2009-11-06T17:25:13Z

UE-InfoVis091 0427422:

== 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]

Other names used for the golden ratio are:
* '''golden section''' (Latin: sectio aurea)
* '''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|]]

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.

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 to us, the Fibonacci-Numbers:

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]]

Talk:Golden Ratio

2009-11-06T17:22:00Z

UE-InfoVis091 0427422:

Golden Ratio

2009-11-06T17:15:33Z

UE-InfoVis091 0427422:

== 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]

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|]]

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.

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 to us, the Fibonacci-Numbers:

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]]

Golden Ratio

2009-11-06T16:57:15Z

UE-InfoVis091 0427422:

== 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]

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|]]

This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.

The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.

{{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 to us, the Fibonacci-Numbers:

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]]

Golden Ratio

2009-11-06T16:54:24Z

UE-InfoVis091 0427422:

== 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]

Two quantities are in golden ration if and only if the following condition holds:
[[Image:golden-ratio.png]]

The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).

It is said that two quantities are in a golden ratio if the following algebraic expression is true:

[[Image:golden-ratio.png]]

[[Image:golden-ratio-graphical.png|right|thumb|upright|]]
In other words if the whole is to the larger as the larger is to the smaller. The golden ratio is irrational mathematical constant. Its value is 1.6180339887... The golden ratio is symbolised by the Greek letter [[Image:Phi.png]] (phi) and also by the less known τ (tau).

This mathematical proportion is often recognized as 'aesthetically pleasing'. Because of that golden ratio found its use in many different fields like mathematics, architecture, geometry, science, biology, nature, art and design.

The actual discovery of the golden ratio can be lead back to the ancient Greeks and the Pythagoras. The greek mathematician Euclid of Alexandria (365BC - 300BC) mentioned the golden mean.

{{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 to us, the Fibonacci-Numbers:

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]]

Talk:Golden Ratio

2009-11-06T16:28:43Z

UE-InfoVis091 0427422: New page: =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 Komment...

=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.

User:UE-InfoVis091 0427422

2009-11-04T15:08:31Z

UE-InfoVis091 0427422: d

== Daniel Scheikl's Userpage ==

=== warrant of apprehension ===
* '''Name:''' Daniel Scheikl
* '''E-Mail:''' daniel.scheikl@student.tuwien.ac.at
* '''web:''' http://cyphorious.net
* '''field:''' Knowledge & Information Management

=== one's best ===
[[{{ns:6}}:Mrolson.jpg]]

=== favourite quote ===
'' "Der Horizont vieler Menschen ist ein Kreis mit Radius Null - und das nennen sie ihren Standpunkt." '' - Albert Einstein

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

2009-10-20T19:40:17Z

UE-InfoVis091 0427422:

== Gruppenmitglieder ==
[[User:UE-InfoVis0910_0827462|Sadauskas, Martin]] 
[[User:UE-InfoVis091_0427422|Scheikl, Daniel]] 
[[User:UE-InfoVis0910_<MATRIKELNR>|<NACHNAME>, <VORNAME>]]

== 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 - Gruppe 13

2009-10-20T19:38:48Z

UE-InfoVis091 0427422:

== Gruppenmitglieder ==
[[User:UE-InfoVis0910_0827462|Sadauskas, Martin]] 
[[User:UE-InfoVis0910_0427422|Scheikl, Daniel]] 
[[User:UE-InfoVis0910_<MATRIKELNR>|<NACHNAME>, <VORNAME>]]

== 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

2009-10-20T19:37:37Z

UE-InfoVis091 0427422:

[[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, <NACHNAME>, Hackl)]]

[[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 09|Gruppe 09 (Hubmann-Haidvogel, Kloibhofer, Riederer)]]

[[Teaching:TUW - UE InfoVis WS 2009/10 - Gruppe 13|Gruppe 13 (Sadauskas, Scheikl, <NACHNAME3>)]]

[[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-InfoVis091 0427422

2009-10-20T19:35:31Z

UE-InfoVis091 0427422:

== Daniel Scheikl's Userpage ==

=== warrant of apprehension ===
* '''Name:''' Daniel Scheikl
* '''E-Mail:''' daniel.scheikl@student.tuwien.ac.at
* '''web:''' http://cyphorious.net
* '''field:''' Software & Information Management

=== one's best ===
[[{{ns:6}}:Mrolson.jpg]]

=== favourite quote ===
'' "Der Horizont vieler Menschen ist ein Kreis mit Radius Null - und das nennen sie ihren Standpunkt." '' - Albert Einstein

User:UE-InfoVis091 0427422

2009-10-20T19:30:10Z

UE-InfoVis091 0427422:

File:Mrolson.jpg

2009-10-20T19:25:39Z

UE-InfoVis091 0427422: Mr. Olson

== Summary ==
Mr. Olson
== Copyright status ==

== Source ==
my private media library ;)

File:1-dbcf279a883314227752fde2cdbd2bcf-m 2.jpg

2009-10-20T19:24:18Z

UE-InfoVis091 0427422: Mr. Olson

== Summary ==
Mr. Olson
== Copyright status ==

== Source ==
My private media library ;)

User:UE-InfoVis091 0427422

2009-10-20T19:15:23Z

UE-InfoVis091 0427422: New page: == Daniel Scheikl's Userpage == === warrant of apprehension === * '''Name:''' Daniel Scheikl * '''E-Mail:''' daniel.scheikl@student.tuwien.ac.at * '''web:''' http://cyphorious.net * '''fi...