golden section (in mathematics), Golden
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golden section
term description
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.
Architecture and Construction
golden section
The division of a line into two segments so
that the ratio of the whole line to the larger
segment equals the ratio of larger segment to the
smaller one; often called the golden section. This
ratio was once considered by some as having an
inherent aesthetic value.
Columbia Encyclopedia
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Golden Section, in mathematics, division of a
line segment into two segments such that the ratio
of the original segment to the larger division is
equal to the ratio of the larger division to the
smaller division. If c is the original segment, b
is the larger division, and a is the smaller
division, then c=a+b and c/b=b/a. Thus, b is the
geometric mean of a and c; the ratio is known as
the Divine Proportion. The Golden Rectangle, whose
length and width are the segments of a line
divided according to the Golden Section, occupies
an important position in painting, sculpture, and
architecture, because its proportions have long
been considered the most attractive to the eye.
The constructions of regular polygons of 5, 10,
and 15 sides depend on the division of a line by
the Golden Section. The numerical ratio of the
greater segment of the line to the shorter segment
as determined by the Golden Section is symbolized
by the Greek letter phi and has the approximate
value 1.618. It occurs in many widely varying
areas of mathematics. For example, in the
Fibonacci sequence (the sequence of numbers formed
by adding successive members to find the next
member—0, 1, 1, 2, 3, 5, 8, 13,...), the values of
the ratios 1, 2/1, 3/2, 5/3, 8/5, 13/8,...
approach the value of the Golden Section.
Bibliography
See H. E. Huntley, The Divine Proportion
(1970).
Golden Section
A mathematical proportion where the ratio
between a small section and a larger section is
equal to the ratio between the larger section and
both sections put together. Used by many 20th
century composers, especially Bela Bartok, to
determine the point of climax for a given work.
Architecture refferal about golden section
McGraw-Hill Dictionary of Architecture and
Construction. Copyright © 2003 by McGraw-Hill
Companies, Inc. All rights reserved. More from
Architecture
* John Loughborough Pearson (architecture)
