My Pythagorean Theorem proof
Remember that (z-s)+s=z, that might help.
Ok, I just realized that you can't see the math...
Well, the box in the middle is a square, with side b. The large triangles have side c and are isosceles. The trapezoids have bases 2a/sqrt3 and a/sqrt3 with height a/sqrt3. With 2 congruent trapezoids. Thus...
2(Atrap)=(Atr+Atr')-Asq
2(1/2)(a/sqrt3)(2a/sqrt3+a/sqrt3)=(c^2/2+c^2/2)-(b^2)
a/sqrt3(3a/sqrt3)=c^2-b^2
3a^2/3=c^2-b^2
a^2=c^2-b^2
a^2+b^2=c^2


Remember that (z-s)+s=z, that might help.
Ok, I just realized that you can't see the math...
Well, the box in the middle is a square, with side b. The large triangles have side c and are isosceles. The trapezoids have bases 2a/sqrt3 and a/sqrt3 with height a/sqrt3. With 2 congruent trapezoids. Thus...
2(Atrap)=(Atr+Atr')-Asq
2(1/2)(a/sqrt3)(2a/sqrt3+a/sqrt3)=(c^2/2+c^2/2)-(b^2)
a/sqrt3(3a/sqrt3)=c^2-b^2
3a^2/3=c^2-b^2
a^2=c^2-b^2
a^2+b^2=c^2
