Pythagorean Theorem XII (visual proof)

This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) following essentially Euclid's proof. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. As a bonus, we show how to use Euclid's shear and rotate proof to create a dissection proof of the Pythagorean theorem. Which of these proofs do you prefer? If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! For other proofs of this same fact check out: https://youtu.be/o2mbN452ywA (compilation) https://youtu.be/XFHm0Ot3PP0 https://youtu.be/q28H5NY5UVU https://youtu.be/yfGtbNgcrQ8 https://youtu.be/JRjPsuJ7S-g https://youtu.be/TsKTteGJpZU https://youtu.be/ZlGaQdNRdqA https://youtu.be/uqGjs_n-f7U https://youtu.be/wWEZ-rUlBDQ https://youtu.be/I75HYC8TRNY https://youtu.be/LWVog8hg74I?si=4GSzTLZP7XIWeaxJ or check out my Pythagorean theorem playlist: https://www.youtube.com/playlist?list=PLZh9gzIvXQUvlRlnYryejWGHYQquM92rB This animation is based on a proof due to Euclid. For a static version of this proof, see Roger Nelsen's first "Proof Without Words: Exercises in Visual Thinking" compendium (page 5) : https://bookstore.ams.org/clrm-1. You can also check out Howard Eves' "Great Moments in Mathematics (Before 1650)" page 31-33. (I may receive a small commission at no cost to you for these affiliate links): https://amzn.to/48mjeX1 https://amzn.to/3Tr0OjW The dissection proof was suggested to me by Glen Whitney (https://studioinfinity.org/), and Glen then found a similar dissection in the compendium of Pythagorean theorem proofs from Elisha Loomis (Proof 21 on p. 122 ). (I may receive a small commission at no cost to you for this affiliate link): https://amzn.to/3RL7rfN #math #pythagoreantheorem #pythagorean #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo To learn more about animating with manim, check out: https://manim.community