The ancient Egyptians found a particular ratio very pleasing to the eye. Their architecture is full of examples of this ratio. And you can see it even in a golden rectangle.

A golden rectangle is one from which, if you remove a square from one end (with side equal to the shorter side of the rectangle), what remains is a rectangle that is similar (has identical proportions) to the original rectangle.

What is the ratio of the longer side, to the shorter side (in the golden rectangle), and how did you determine it?
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By the way, I realize many people are familiar with this ratio (in which case this is a very easy problem), but for those who haven't, do them a favor, and please don't post the solution.

(In reply to Golden Section - an interesting number by retiarius)

To continue with my answer (because nobody else did) the equation can be multiplied by y/x by both sides, and 1 can be subtracted from both sides to give:

(y/x)² - (y/x) -1 = 0; and since this is quadratic, solving with the quadratic formula gives: (1±√(5))/2

This makes sense because if you multiply (√(5) -1)/2 by (√(5)+1)/(√(5)+1) it will stay equal (you are multiplying by 1), but you will get (5-1)/(2(√(5)+1)) or 4/(2(√(5)+))), or 2/(√(5)+1)

Posted by Gamer on 2003-11-27 07:50:33