Proving the Pythagorean theorem

We will now prove the Pythogorian theorem: $a^2+b^2=c^2$

We can prove the theorem algebraically by showing that the area of the big square equals the area of the inner square (hypotenuse squared) plus the area of the four triangles: $\begin{array}{rcl}{(a+b)}^2& =& c^2+4\cdot \left(\frac{1}{2}ab\right)\\ a^2+2ab+b^2& =& c^2+2ab\\ a^2+b^2& =& c^2\end{array}$