I stumbled upon this old post from Iñigo Quilez, and this made my day. Especially because I did not know about the Babylonian multiplication, let alone its proof. The absence of explanation in the post made it into a nice puzzle, I had to figure things out by myself. Maths teaching should more often be like this kickstarted discovery...
Related: <a href="https://en.wikipedia.org/wiki/Proof_without_words" rel="nofollow">https://en.wikipedia.org/wiki/Proof_without_words</a><p>Unfortunately the metamathematics of wordless proofs still needs words, maybe someone can make a proof theory without words?<p><a href="https://www.maa.org/press/periodicals/convergence/proofs-without-words-and-beyond-pwws-and-mathematical-proof" rel="nofollow">https://www.maa.org/press/periodicals/convergence/proofs-wit...</a>
The idea would be more obvious if `a` woldn't be exactly `2b` in this example (granted, author wasn't at liberty to choose values). Being previously unaware of what is Babylonian multiplication, it took me quite some time to get what exactly is being conveyed. It is too tempting to read it as "2 x 1" in this case, which doesn't register as a very notable generic discovery. I suspect many people who would find it otherwise interesting simply passed by before understanding what he is trying to show us.