Pythagorean Theorem II (visual proof)

This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using a dissection of a square in two different ways. 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. #mathshorts #mathvideo #math #pythagoreantheorem #pythagorean #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof

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Background music, used according to CC BY-SA 3.0, is "The Road" from Esteban Orlando:

Esteban Orlando:

[louisvictor]

A feature I find fascinating about this is that it demonstrates the internal consistency of maths. Once you get to the square of sides a+b at about 0:43, you can also get to the formula through a more algebraic path if that is your jam, but the important part is that if math is internaly consistent the two results must be equal in the end. And of course they are. The big square's area is (a+b)^2, which is the sum of the c^2 square and the the area of each of the 4 triangles which is ([a+b]^2)/2, so if you set the equation (a+b)^2 = 4 * ([a*b]/2 ) + c^2, develop it, isolate C^2 and simplify, you get exactly c^2 = a^2 + b^2 that way too.

[DrWeselcouch]

My favorite proof of the Pythagorean theorem!

[CrusaderGeneral]

why dont they teach this in basic school, instead they force you to memorize it, and I can almost guarantee that the teachers themselves never learned this

[theultimatereversecard]

theres no reason why math should be overhated