(1/5) There are hundreds of proofs of the Pythagorean theorem, some remarkably simple. Here’s on I just typed up.

Start with any right triangle:

(2/5) Now scale this triangle three times: once by a factor of b, once by a factor of c, and once by a factor of a:

(3/5) Now rotate and/or mirror these, to get this:

(4/5) Finally, piece them together to get the following rectangle. And it is a rectangle, since the two non-right angles of a triangle add up to 90°.

(5/5) For rectangles, the top side and the bottom side must be equal, giving us the result!