Sum of Cubes IV (Nicomachus's Theorem)

Описание: 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...  

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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/...