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