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 distance from the floor to the navel [h.sub.B] was measured for the purpose of calculating the real value of ratio h/[h.sub.B] for the golden section, for all groups of respondents.
As a line search method which is implemented without using derivatives for the targeted function for finding an optimal value that maximizes or minimizes the function, the basic concept of golden section method (GSM) is to reduce the interval of uncertainty during the search procedure to fix a point for minimizing, in this research, the given function.
Golden section search is an optimization technique that can be used to find the maximum or minimum value of a single unimodal function.
We adopt golden section method to compute [[alpha].sub.(i,j)] according to the formula (26) and then begin to repeat inner loop.
Even so, a 1, a2, and a3 are nearly accordant with the characteristic of the golden curve introduced in Introduction, and we could also draw the conclusion that there are many functional partitions which are accordant with the golden section and the "golden curve" on human upper limbs.
Substitute [??] and [??] into the primary cost function (21a), the constant [??] can be worked out by golden section method.
Golden Section Search enables an iterative adjustment of the trajectory in each step by using the calculated parameter [C.sub.x] for every previous iteration.
Golden section also appears as a growing pattern in different biological systems (Doczi, 1996; Hemenway, 2008).
The objective of optimization design is to find the optimal main wavelength of design, corresponding to the maximal energy efficiency, which can be potentially realized via an iterative search, such as the well-known golden section search method.
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.
The Fibonacci Sequence and the Golden Section in Electrical Engineering and Numerical Analysis
The case b = 1 corresponds to co-called golden section. Farther calculations on the base of (9) give:
For more contemporary flavor, the company tackles Twyla Tharp's athletic The Golden Section. Then the full company canters through all four movements of Balanchine's Western Symphony, with no curtain coming down to save the dancers from the showstopping finale of pirouettes (corps member Rebecca King reported on her blog, www.tendusunderapalmtree.com, that the dancers had to film the turn sequence seven times--that's a lot of releves!).
in their growth," (3) a concept that resonates in Rockburne's love of dance and its similarities with the Golden Section. She writes how dancing "taught me the way the body folds" (137).
With the four featured paintings of identical formats and sizes (78 by 86 inches) in the main gallery space, Baker employs the familiar yet effective Golden Section in her composition.