Here is a proof of Pythagoras using a geometric series: https://www.cut-the-knot.org/pythagoras/Proof100.shtml https://www.cut-the-knot.org/pythagoras/Proof100

Here is a proof of Pythagoras using a geometric series: https://www.cut-the-knot.org/pythagoras/Proof100.shtml https://www.cut-the-knot.org/pythagoras/Proof100.shtml The proof is by John Arioni and also features an infinite number of similar triangles.