Geometric Visualization of the Sum of the First n Squares

This is a short, animated visual proof of the formula that computes that sum of the first n squares using 6 copies of the sum of squares pyramids to build a rectangular prism .

Here is a slower version of this video:

https://youtu.be/WidzHiUFWNA

Here are three other visual proofs about the sum of squares formulas:

https://youtu.be/-tJhH_k2LaM
https://youtu.be/UqVmocdLFGc
https://youtu.be/Q-frL0Ot2m4

This animation is based on a visual proof by Man-Keung Siu from the March 1984 issue of Mathematics Magazine (https://www.jstor.org/stable/2689589), page 92.

To learn more about animating with manim, check out:
https://manim.community

#math #manim​ #mathvideo​​ #sumofsquares​ #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath

This is my version of a classic visual proof. Here are other renditions:
https://youtu.be/aXbT37IlyZQ by @ThinkTwiceLtu
https://youtu.be/lqGVefx-HJw by @Mathocube
https://youtu.be/NZaEQFn1LGY by @MathPhysicsEngineering