golden section


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golden section

n.
A ratio, observed especially in the fine arts, between the two dimensions of a plane figure or the two divisions of a line such that the smaller is to the larger as the larger is to the sum of the two, a ratio of roughly three to five. Also called golden ratio.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

golden section

or

golden mean

n
(Art Terms) the proportion of the two divisions of a straight line or the two dimensions of a plane figure such that the smaller is to the larger as the larger is to the sum of the two. If the sides of a rectangle are in this proportion and a square is constructed internally on the shorter side, the rectangle that remains will also have sides in the same proportion. Compare golden ratio
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

gold′en sec′tion


n.
a ratio between two portions of a line, or the two dimensions of a plane figure, in which the lesser of the two is to the greateras the greater is to the sum of both: a ratio of approximately 0.618 to 1.000.
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.golden section - the proportional relation between two divisions of line or two dimension of a plane figure such that short : long :: long : (short + long)
golden mean
proportion - the quotient obtained when the magnitude of a part is divided by the magnitude of the whole
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
sezione aurea
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References in periodicals archive ?
"This piece is governed by Fibonacci numbers (a series of numbers created by adding up the two numbers before it) and a golden section (a special number which can be found by looking at the ratio of two Fibonacci numbers).
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'The arabesque', he says, 'represents at once linear time and circular time, because it goes backwards while moving further forward.' Most prominently, it has led to a fascination with the Golden Section, the never-ending (or 'irrational') number that has so occupied mathematicians from Euclid onwards, and that has engrossed so many artists and architects.
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More importantly, for the first time, two new estimation algorithms are proposed to improve a way of finding an optimal step size by incorporating a golden section method (GSM) into general routine of both DFP and BFGS.
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[x.sub.1] and [x.sub.2] are the coefficients obtained by the golden section method.
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For a given [P.sub.(i,j)], [[phi].sub.i,j] and [tau], a joint resource allocation scheme for [P.sub.(i,j).sup.S 3] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to maximize [R.sub.(i,j) is proposed where the [P.sub.(i,j).sup.TS 2] and [P.sub.(i,j).sup.TS 3] can be easily obtained by golden section method to search a optimal [[eplison].sub.(i,j)].
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The golden ratio ([approximately equal to] 1.618), sometimes known as the golden section or golden number, has been fascinating philosophers, scientists, and artists for more than two millennia [1-4].
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Taking amplitude difference into account, golden section method is applied to seek an appropriate amplitude factor.
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In order to find the optimum, one of the fastest methods of one-dimensional optimization, the so-called "Golden Section Search," is applied.
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Creation is suffused with underlying and deliberate structures--one example, the golden section, is found universally, from genetic sequencing to galaxies, in the construction of flowers, insects, and the human form.
Beyond depiction: Sophie Hacker gives an introduction to sacred geometry in the Christian tradition and in her own artistic practice
As stated by Pacioli (1509/1991), the golden section is defined as a harmonic division of a line in extreme and mean ratio (see the top panel of Figure 1).
Aproximacion experimental al estudio de la belleza: El papel de la proporcion aurea

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