The ancient Greeks, being masters of geometric manipulation, often tried their hand at "squaring" various shapes. This involved using only the most fundamental rules of geometry to construct a square whose area equals the area of the original shape.

Can you follow in their footsteps and square a simple triangle?

The solution must hold for all types of triangles.

Euclid's II.14 (Book II, Proposition 14) solves this problem.

Googling Euclid II.14 gives many interesting links, among them in particular is the reasonably understandable

http://www.headmap.org/unlearn/euclid/book2/2.14.htm

Posted by Richard on 2004-09-24 00:42:11