Uploaded August 2024 | Updated September 2026, 2 weeks ago

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This is a short, animated (wordless) visual proof demonstrating the sum of the first n positive cubes by rearranging two stacks of cubic arrays.

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

youtu.be/LYfKapE_g1Q
youtu.be/jWpyrXYZNiI
youtu.be/YQLicI8R4Gs
youtu.be/Ye9OPNqV9FA
youtu.be/NxOcT_VKQR0
youtu.be/d1yM6Rq7Tfw

This animation is based on a visual proof by Tom Edgar from the September 2024 issue of Mathematics Magazine (doi.org/10.1080/0025570X.2024.2379213 page ??).

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

#mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath #calculus #sum #induction #faulhaber #sumofcubes #cubes
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Music in this video:
Epic Cyberpunk | GLORY by Alex-Productions | https://onsound.eu/
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Creative Commons / Attribution 3.0 Unported License (CC BY 3.0)
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