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Golden Ratio (Posted on 2003-11-26) Difficulty: 3 of 5
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.

See The Solution Submitted by SilverKnight    
Rating: 3.0000 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution A way to solve this | Comment 2 of 9 |
The idea here is that from a rectangle dimensions x by y, y-x is to x as x is to y, by the proportion given information.

(y-x)/x = x/y, which equals y/x - 1 = x/y. In other words, the ratio is equal to 1 more than its reciprocal.
  Posted by Gamer on 2003-11-26 16:20:12
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