- Root rectangle
In
geometry , a root rectangle isrectangle in which the ratio of the longer side to the shorter is thesquare root of aninteger , such as √2, √3, etc.cite book
author=Jay Hambidge
authorlink=Jay Hambidge
title=Dynamic Symmetry: The Greek Vase
publisher=Yale University Press
year=1920
pages=pp. 19–29
url=http://books.google.com/books?id=Qq4gAAAAMAAJ&pg=PA40&dq=dynamic-rectangles+inauthor:hambidge&lr=&as_brr=0&ei=3MFBSJeKLI7iiwHRtY2JBQ#PPA44,M1 (or 2003 reprint from Kessinger Publishing, Whitefish, MT, ISBN 0-7661-7679-7) ]The root-2 rectangle is constructed by extending two opposite sides of a
square to the length of the square's diagonal. The root-3 rectangle is constructed by extending the two longer sides of a root-2 rectangle to the length of the of the root-2 rectangle's diagonal. Each successive root rectangle is produced by extending a root rectangle's longer sides to equal the length of that rectangle's diagonal.Jay Hambidge. (1926, 1948, 1967)" [http://books.google.com/books?id=VYJK2F-dh2oC&pg=PA10&dq=intitle:dynamic+intitle:symmetry+inauthor:hambidge+root+dynamic-rectangles&lr=&as_brr=0&ei=b0BCSJHNBZW-jgG6gsGIBQ&sig=fE_8Kx_rO0GURo3g6JLizq1MUsI#PPA9,M1 The Elements of Dynamic Symmetry] ". Courier Dover Publications. pp. 9–10.]Dynamic rectangles
Jay Hambidge , as part of his theory of dynamic symmetry, includes the root rectangles in what he calls "dynamic rectangles", which have irrational and geometricfraction s as ratios, such as thegolden ratio or square roots. Hambidge distinguishes these from rectangles with rational proportions, which he terms "static rectangles".cite book
author = Matila Ghyka
year = 1977
title = The Geometry of Art and Life
publisher=Courier Dover Publications
pages =pp. 126–127
url=http://books.google.com/books?id=Qq4gAAAAMAAJ&pg=PA40&dq=dynamic-rectangles+inauthor:hambidge&lr=&as_brr=0&ei=3MFBSJeKLI7iiwHRtY2JBQ] According to him, root-2, 3, 4 and 5 rectangles are often found in Gothic and Classical Greek and Roman art, objects and architecture, while rectangles with aspect ratios greater than root-5 are seldom found in human designs.According to
Matila Ghyka , Hambidge's dynamic rectanglesProperties
*When a root-"N" rectangle is divided into "N" congruent rectangles by dividing the longer edge into "N" segments, the resulting figures keep the root-"N" proportion (as illustrated above). [cite book | title = Book Design | author = Andrew Haslam | publisher = Laurence King Publishing | year = 2006 | isbn = 1856694739 | url = http://books.google.com/books?id=_Ri63jEKPfgC&pg=PT27&dq=root-rectangle&as_brr=3&ei=N2wySKOPL4uKtAOk2NnvAg&sig=98V_Ww1L3EgAKmPofmkscnvxMsk ]
*The root-3 rectangle is also called "sixton", [Wim Muller (2001) "Order and Meaning in Design". Lemma Publishers, p. 49.] and its short and longer sides are proportionally equivalent to the side and diameter of a
hexagon .Kimberly Elam (2001) "Geometry of Design: Studies in Proportion and Composition. Princeton Architectural Press." ISBN:1568982496.]*Since 2 is the square root of 4, the root-4 rectangle has a proportion 1:2, which means that it is equivalent to two squares side-by-side.
*The root-5 rectangle is related to the
golden ratio . The longer side is equal to one plus two times 1/φ (0.618...).*The root-φ rectangle is a dynamic rectangle but not a root rectangle. Its diagonal equals φ times the length of the shorter side. If a root-φ rectangle is divided by a diagonal, the result is two congruent
Kepler triangle s.ee also
*
Square root of 2
*Square root of 3
*Square root of 5 References
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