Natural Number

This is a short, animated visual proof giving a formula for the sum of the first n positive cubes. #mathshorts​ #mathvideo​ #math​ #numbertheory #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #cubes #mathematics #sum This animation is based on a visual proof by Georg Schrage from the June 1992 issue of Mathematics Magazine (https://doi.org/10.2307/2691330 - page 185). To learn more about animating with manim, check out: https://manim.community __________________________________________________________________ Background music, used according to CC BY-SA 3.0, is "The Road" from Esteban Orlando: Esteban Orlando: https://soundcloud.com/orlando-esteba... https://www.instagram.com/estebanorla... https://creativecommons.org/licenses/... Music provided by RFM: https://youtu.be/b4KCM1bIq50