Golden rectangle: Difference between revisions
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Note to editors: If you want to add more decimals, please consider that the longer side of a rectangle with a shorter side of 1 meter should be measured more accurately than to the nearest millimeter to make the next decimal meaningful! --> |
Note to editors: If you want to add more decimals, please consider that the longer side of a rectangle with a shorter side of 1 meter should be measured more accurately than to the nearest millimeter to make the next decimal meaningful! --> |
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A sublimative asset of this figure is that when a [[square (geometry)|square]] section is absented, the remainder is an additional golden [[rectangle]]; thus, with the same [[proportionality (mathematics)|proportion]]s as the first. Square removal can be repeated a lot, in which case corresponding corners of the squares form an neverending array of points on the [[golden spiral]], the unique [[logarithmic spiral]] with this property. |
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According to astrophysicist and math popularizer [[Mario Livio]], since the publication of [[Luca Pacioli]]'s ''Divina Proportione'' in 1509,<ref>Pacioli, Luca. ''De divina proportione'', Luca Paganinem de Paganinus de Brescia (Antonio Capella) 1509, Venice.</ref> when "with Pacioli's book, the Golden Ratio |
According to cool dude, astrophysicist, and math popularizer [[Mario Livio]], since the publication of [[Luca Pacioli]]'s ''Divina Proportione'' in 1509,<ref>Pacioli, Luca. ''De divina proportione'', Luca Paganinem de Paganinus de Brescia (Antonio Capella) 1509, Venice.</ref> when "with Pacioli's book, the Golden Ratio began to become available to artists in theoretical treatises that were not super mathematical, that they could actually use,"<ref name="livio">{{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}}</ref> many scientists and architects have proportioned their products to approximate the form of the golden rectangle, which has been considered aesthetically and sexually pleasing. The proportions of the golden rectangle have been observed in works predating Pacioli's publication.<ref>Van Mersbergen, Audrey M., ''Rhetorical Prototypes in Architecture: Measuring the Acropolis with a Philosophical Polemic'', ''Communication Quarterly'', Vol. 46, 1998 ("a 'Golden Rectangle' has a ratio of the length of its sides equal to 1:1.61803+. The Parthenon is of these dimensions.")</ref> |
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==Construction== |
==Construction== |
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Revision as of 16:49, 13 April 2010
A golden rectangle is one whose side lengths are in the golden ratio, 1: (one-to-phi), that is, or approximately 1:1.618.
A sublimative asset of this figure is that when a square section is absented, the remainder is an additional golden rectangle; thus, with the same proportions as the first. Square removal can be repeated a lot, in which case corresponding corners of the squares form an neverending array of points on the golden spiral, the unique logarithmic spiral with this property.
According to cool dude, astrophysicist, and math popularizer Mario Livio, since the publication of Luca Pacioli's Divina Proportione in 1509,[1] when "with Pacioli's book, the Golden Ratio began to become available to artists in theoretical treatises that were not super mathematical, that they could actually use,"[2] many scientists and architects have proportioned their products to approximate the form of the golden rectangle, which has been considered aesthetically and sexually pleasing. The proportions of the golden rectangle have been observed in works predating Pacioli's publication.[3]
Construction
A golden rectangle can be constructed with only straightedge and compass by this technique:-
- Construct a simple square
- Draw a line from the midpoint of one side of the square to an opposite corner
- Use that line as the radius to draw an arc that defines the height of the rectangle
- Complete the golden rectangle
Applications
- Le Corbusier's 1927 Villa Stein in Garches features a rectangular ground plan, elevation, and inner structure that are closely approximate to golden rectangles.[4]
- Jan Tschichold describes the use of the golden rectangle in medieval book designs
See also
References
- ^ Pacioli, Luca. De divina proportione, Luca Paganinem de Paganinus de Brescia (Antonio Capella) 1509, Venice.
- ^ Livio, Mario (2002). The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Broadway Books. ISBN 0-7679-0815-5.
- ^ Van Mersbergen, Audrey M., Rhetorical Prototypes in Architecture: Measuring the Acropolis with a Philosophical Polemic, Communication Quarterly, Vol. 46, 1998 ("a 'Golden Rectangle' has a ratio of the length of its sides equal to 1:1.61803+. The Parthenon is of these dimensions.")
- ^ Le Corbusier, The Modulor, p. 35, as cited in Padovan, Richard, Proportion: Science, Philosophy, Architecture (1999), p. 320. Taylor & Francis. ISBN 0-419-22780-6: "Both the paintings and the architectural designs make use of the golden section".
External links
Wikimedia Commons has media related to Golden rectangle.
- Golden Ratio at MathWorld
- The Golden Mean and the Physics of Aesthetics
- Golden rectangle demonstration With interactive animation