(mathematics) A rectangle that can be divided into a square and another rectangle similar to itself; its sides have the ratio (1+√5)/2.
Golden rectangle
| Sci-Tech Dictionary: golden rectangle |
(′göl·dən ′rek′taŋ·gəl)
| 5min Related Video: Golden rectangle |
| Architecture and Landscaping: golden rectangle |
The basis of standardized sizes of components, in which the ratio of width to length is the same as that of length to the sum of the width and length.
| Wikipedia: Golden rectangle |
This article is about the geometrical figure. For the Indian highway project, see Golden Quadrilateral.
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 distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle; that is, with the same proportions as the first. Square removal can be repeated infinitely, in which case corresponding corners of the squares form an infinite sequence of points on the golden spiral, the unique logarithmic spiral with this property.
According to 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 started to become available to artists in theoretical treatises that were not overly mathematical, that they could actually use,"[2] many artists and architects have proportioned their works to approximate the form of the golden rectangle, which has been considered aesthetically pleasing. The proportions of the golden rectangle have been observed in works predating Pacioli's publication.[3]
Contents |
Construction
, the golden ratio.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
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
| Best of the Web: Golden rectangle |
Some good "Golden rectangle" pages on the web:
 Math mathworld.wolfram.com |
Learn More
 | golden number |
| Golden Section (in mathematics) |
| Donald in Mathmagic Land (1959 Film) |
 | What logos have the golden rectangle? Read answer... |
| When was the golden rectangle first used? Read answer... |
| Explain the term Golden rectangle? Read answer... |
Help us answer these
 | Who discovered the golden rectangle? |
| Where are golden rectangles used in architecture? |
| Who created the golden rectangle? |
Post a question - any question - to the WikiAnswers community:
Copyrights:
 |
 | Sci-Tech Dictionary. McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved. Read more |
 |
| Architecture and Landscaping. A Dictionary of Architecture and Landscape Architecture. Copyright © 1999, 2006 by Oxford University Press. All rights reserved. Read more |
 |
| Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Golden rectangle". Read more |
