the golden section


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golden section

A division in a line such that the proportion of the whole to the larger area is equal to the proportion of the larger area to the smaller one. The mathematical golden section has been employed in all manner of things, not the least in art, architecture, and even philosophy.
See also: golden, section

the golden section

the division of a line so that the whole is to the greater part as that part is to the smaller part.
This is a mathematical term for a proportion known since the 4th century and mentioned in the works of the Greek mathematician Euclid. It has been called by several names, but the mid 19th-century German one goldene Schnitt , translating Latin sectio aurea , has given rise to the current English term.
See also: golden, section
References in periodicals archive ?
'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.
In this research, we adopted the golden section method (GSM) as a line search tool.
[x.sub.1] and [x.sub.2] are the coefficients obtained by the golden section method.
According to (26) and applying the golden section method in [20], the optimization [[eplison].sub.(i,j)] can be achieved.
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].
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).
Introducing the golden section rule in the architecture, the concept of the perfect proportion of the elements that constitute the spatial spherical structures has developed.
Vajda: Fibonacci and Lucas numbers, and the Golden Section: Theory and Applications, 1989, Dover Publications, Inc., Mineola, 2008.
(2) Calculate the golden section points of [[lambda].sub.m3] and [[lambda].sub.m4].(3) Determine whether the utilized energy efficiency [[eta].sub.m3] equals [[eta].sub.m4] and whether [[lambda].sub.m3] equals [[lambda].sub.m4].
We will prove that the complete affine fullerene [C.sub.60] can be presented only by means of the golden section. The concept of a GS-quasigroup will be used in this consideration.