Visual Proof of Summing Cubes Without Words #phonk #phonkmath

This is a short, animated (wordless) visual proof demonstrating the sum of the first n positive cubes by rearranging cubes into a flat square.

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Here is a longer version of this proof : https://youtu.be/YQLicI8R4Gs

Here are three other visual proofs of sum of cubes formulas:

https://youtu.be/Ye9OPNqV9FA
https://youtu.be/NxOcT_VKQR0
https://youtu.be/d1yM6Rq7Tfw

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.

This is my version of a classic visual proof. Here are other renditions:
https://youtu.be/glearwgR1Ls by @ThinkTwiceLtu
https://youtu.be/YG_gS5vZoyQ by @Mathocube
https://youtu.be/WY5X_3q80WY by @Mathologer

#mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath #calculus #sum #induction

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