Given any right triangle you can create a figure like the one above using four
of them. This is because the sum of the three angles
always is 180 degrees. The area of the outside square is c^{2}.
We can also find the area by summing the area of the individual
parts: 4*(a*b/2)+(a-b)^{2} = 2ab + a^{2} -2ab + b^{2}
= a^{2} + b^{2}. Thus a^{2} + b^{2} =
c^{2}.

I didn't assign a diffulty level because I saw Carl Sagan explain this proof on television so I never had a chance to solve it myself.

Michael Shackleford, A.S.A.