## A Visual Proof of the Pythagorean Theorem in D3

6 July 2018

Slide the green dot up and down the left hand side of the canvas.

We have two squares that are the same size. If they are the same size, then they must have the same area. The two squares on the left side represent \( a^2 \) and \( b^2 \), and the square on the right is \( c^2 \). Each triangle is a right triangle with legs of length \( a \) and \( b \). That means that each triangle has area \( \frac{1}{2} ab \).

\begin{align}
\left( left \right) ^ {2} &= \left( right \right) ^ {2} \

\left( a + b \right) ^ {2} &= c^{2} + 4 \times \left( \frac{1}{2} ab \right) \

a^{2} + 2ab + b^{2} &= c^{2} + 2ab \

a^{2} + b^{2} &= c^{2} \

\end{align}

Thatâ€™s it. Have fun playing!