Sum of Cubes IV (Nicomachus's Theorem)

This is a short, animated (wordless) visual proof demonstrating the sum of the first n positive cubes by rearranging cubes into a flat square. #mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath #calculus #sum #induction Here are three other visual proofs of sum of cubes formulas:    • Visual Sum of Cubes II      • Sum Of Cubes I (visual proof)      • Visual Sum of Cubes III   This animation is based on independently discovered, separate visual proofs by J. Barry Love from the March 1977 issue of Mathematics Magazine (https://www.jstor.org/stable/2689727), page 74, and Alan L. Fry from the January 1985 issue of Mathematics Magazine (https://www.jstor.org/stable/2690228) , page 11. To learn more about animating with manim, check out: https://manim.community This is my version of a classic visual proof. Here are other renditions:    • Nicomachus's theorem | Visualisation | 3-D...   by ‪@ThinkTwiceLtu‬    • Nicomachus's theorem | visual proof | math...   by ‪@Mathocube‬ Edit: and thanks to a viewer I learned that ‪@Mathologer‬ posted a similar video a day ago :    • Animating Nicomachus's 2000 year old mathe...   ___________________________________________ Music in this video: Rain On The Window by Alex-Productions | https://onsound.eu/ Music promoted by https://www.free-stock-music.com Creative Commons Attribution 3.0 Unported License https://creativecommons.org/licenses/...