Golden rectangle

From Example Problems
Jump to navigation Jump to search
File:Golden rectangle detailed.png
The large rectangle BA is a golden rectangle. If we remove square B, what is left, A, is another golden rectangle.

A golden rectangle is a rectangle with dimensions which are of the golden ratio, 1 : φ (i.e., 1.6180339887498948...). It yields another rectangle with sides of the same proportions when sectioned in a particular manner. That is, sectioned into two shapes: firstly a square with one side being one of the lesser sides of the surrounding golden rectangle; and secondly a rectangle composed of the remainder. The new, smaller rectangle is thus a golden rectangle itself, and one of its longer sides will be the other lesser side of the surrounding rectangle, the other being one of the sides of the new square.

The rectangle looks like this:

φ = 1 + x
x = φ - 1
φ 1 x = 1 / φ
File:Golden rectangle.png 1 199px 1

See also

External links

sk:Zlatý obdĺžnik sl:Zlati pravokotnik zh:黄金矩形