May 29, 2020
Not-Puzzle #2
Made this animated proof of Pythagoras’ theorem using the principle of similar triangles:
Based off of 3Blue1Brown’s visualisation for cos² θ + sin² θ = 1 - since that identity is a special case of Pythagoras’ Theorem, I thought I’d generalise it to any right-angled triangle.
Dropping a perpendicular from the right angle lets us split the hypotenuse h into two sections, which I’ve labelled hx and hy here - and the whole equals the sum of the parts. Checking the angles shows us that we now have three similar right-angled triangles, and ratios for the side lengths of these triangles. Some rearrangement and substitution gives us Pythagoras’ theorem!
