Maths and art part 2: Golden Rectangles

I would like to copy-paste this article as I found it. One does not retouch/edit a classic.

I could not help myself to add one comment.

Enjoy.

Golden Rectangles

The golden rectangle R, constructed by the Greeks, has the property that when a square is removed a smaller rectangle of the same shape remains. Thus a smaller square can be removed, and so on, with a spiral pattern resulting. (Mondrian, hey?)

 

The Greeks (the Geeks. Full stop.) were thus able to see geometrically that the sides of R have an irrational ratio, 1 : x. The smaller rectangle has sides with ratio 1-x : 1; since this is the same as the ratio for the big rectangle, one finds that x^2 = x+1 and thus x = (1+Sqrt(5))/2 = 1.618033989....

The golden rectangle was considered by the Greeks to be of the most pleasing proportions, and its shape figures in ancient architecture.

The same motif is used in modern architecture such as the buildings of Le Corbusier (whose only work in North America is the Carpenter Center at Harvard).