Golden Mean
The Golden Mean, or Golden Ratio, is an aspect ratio
(width v. height) that predates Greek architecture. Many
think this is the most pleasing ratio for a design of
paintings, particularly of horizontal landscapes.
Psychologists have verified this in empirical tests.
I explored the use of the Golden Mean in my painting,
Fibonacci’s Golden Tree. The sheet of watercolor paper,
the painted image, as well as all rectangles in the painting
(including the sides of the birdhouse) are sized to the
Golden Mean.
Italian mathematician Fibonacci (whose real name was
Leonardo of Pisa) developed his well-known series, which, in
turn, is a key to the Golden Mean. This series is described
and shown in the border of my painting. The series is
simple. Starting with 0 and 1, each successive term is the
sum of the preceding two. Zero plus 1 equals 1; 1 plus 1
equals 2; 2 plus 1 equals 3, 2 plus 3 equals 5, etc. The
series is then 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ad
infinitem. As these sequential terms get large, the ratio of
any two successive terms approaches the Golden Mean.
(width v. height) that predates Greek architecture. Many
think this is the most pleasing ratio for a design of
paintings, particularly of horizontal landscapes.
Psychologists have verified this in empirical tests.
I explored the use of the Golden Mean in my painting,
Fibonacci’s Golden Tree. The sheet of watercolor paper,
the painted image, as well as all rectangles in the painting
(including the sides of the birdhouse) are sized to the
Golden Mean.
Italian mathematician Fibonacci (whose real name was
Leonardo of Pisa) developed his well-known series, which, in
turn, is a key to the Golden Mean. This series is described
and shown in the border of my painting. The series is
simple. Starting with 0 and 1, each successive term is the
sum of the preceding two. Zero plus 1 equals 1; 1 plus 1
equals 2; 2 plus 1 equals 3, 2 plus 3 equals 5, etc. The
series is then 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ad
infinitem. As these sequential terms get large, the ratio of
any two successive terms approaches the Golden Mean.
| home . . . paintings . . . projects . . . artist profile . . . contact me |
| All paintings are copyright by Herb Reed and may not be reproduced without the written permission of the artist. |
| Whatever creativity is, it is in part a solution to a problem. Brian W. Aldiss |
The Golden Mean (G) is derived using two lines lengths Y and X.
_____________________________ ___________________
Y X
G = (Y + X)/Y = Y/X, or Y = GX. Therefore,
(XG + X)/ XG = XG/X, or (G + 1)/ G = G. Thus, G squared - G -1 = 0. This is a Quadratic
Equation. Solving this yields . . .
G = (1 + Sq.Rt.(12 + 4))/2 {for the positive root}, or
G = (1 + Sq.Rt.(5))/2 = 1.6180339887. . . .
If you take a higer term of Fibonacci’s series (e.g. 6,765), and divide it into the following term
(10,946), the result is 1.6180339.
