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.

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

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.
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)
proportion - the quotient obtained when the magnitude of a part is divided by the magnitude of the whole
Translations
sezione aurea
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).
'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.
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.
[x.sub.1] and [x.sub.2] are the coefficients obtained by the golden section method.
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)].
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].
Taking amplitude difference into account, golden section method is applied to seek an appropriate amplitude factor.
In order to find the optimum, one of the fastest methods of one-dimensional optimization, the so-called "Golden Section Search," is applied.
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.
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).