Uploads from Mathematical Visual Proofs

Currently Playing: Geometric Mean Theorem (Visual Proof)

This is a short, animated visual proof showing what is known as the geometric mean theorem, which provides a relation between the altitude on the hypotenuse of a right triangle and the two lengths created by that altitude on the hypotenuse. In particular, the height is the square root of the product of those two lengths. Here we show a classic visual proof using dissection and rearrangement. I could not find an original source for this visual proof, but you can see a static version on the wikipedia site: https://en.wikipedia.org/wiki/Geometric_mean_theorem If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! ​#math​ #mathematics​ #manim​ #​proofwithoutwords #visualproof​ #geometricmean #righttriangle #geometry #area #triangle #dissection #geometric To learn more about animating with manim, check out: https://manim.community