Summing cubes without words
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 : • Sum of Cubes IV (Nicomachus's Theorem)
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.
This is my version of a classic visual proof. Here are other renditions:
• Nicomachus's theorem | Visualisation ... by @ThinkTwiceLtu
• Nicomachus's theorem | visual proof |... by @Mathocube
• Animating Nicomachus's 2000 year old ... by @Mathologer
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To learn more about animating with manim, check out:
https://manim.community
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