Pythagorean theorem from a (semi) circle! @MathVisualProofs

Uploaded June 2024 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the semicircle and Thales triangle theorem. 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.

This animation is based on a proof due to Michael Hardy from the November, 1986 issue of The College Math Journal (doi.org/10.2307/2686255).

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For other proofs of this same fact check out the following playlist:

youtube.com/playlist?list=PLZh9gzIvXQUvlRlnYryejWGHYQquM92rB&si=o_im7-_NHp1zhkcD
#mathshorts #mathvideo #math #pythagoreantheorem #pythagorean #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof

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Pythagorean theorem from a (semi) circle!

$Chaos Game finds the Mandelbrot Quintet In this video, we show how to use a random process of iteratively applying five affine transformations in the real plane to generate a 5-rep-tile known as the Mandelbrot Quintet. What happens if you do something similar with different affine transformations? Here is a bit longer version (without words): https://youtu.be/rLxx6b-oJGo Check out these videos for related constructions: https://youtube.com/shorts/dklWNdM9WSg https://youtu.be/rLxx6b-oJGo https://youtu.be/NBI_5GdvqUo If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! This animation was inspired by an article written by Lorelei Koss that appeared in the Proceedings of Bridges 2015: https://archive.bridgesmathart.org/2015/bridges2015-423.pdf . For more information, you should also check out the related article Fractal Tilings in the Plane by Richard Darst, Judith Palagallo and Thomas Price from the February 1998 Mathematics Magazine: https://www.jstor.org/stable/2691339 #chaos #chaosgame #quintet #mandelbrot #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractals To learn more about animating with manim, check out: https://manim.community$

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