Sums of Sums of Squares (visual proof) @MathVisualProofs

Uploaded September 2024 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof for the sum of the sum of squares formula using a wonderful visual proof computing the sum of squares formula.

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Here is a link to the visual proof for the sum of squares:
youtu.be/-tJhH_k2LaM

Here are other visual proofs about the sum of squares formulas:

youtu.be/a8j3sBrXchg
youtu.be/WidzHiUFWNA
youtu.be/UqVmocdLFGc
youtu.be/Q-frL0Ot2m4
youtu.be/VYaEGvClg7Q

This animation is based on a visual proof by C.G. Wastun according to Roger Nelsen in his second Proof without Words compendium (page 91) : bookstore.ams.org/view?ProductCode=CLRM/14

This first visual proof animation is based on (independently discovered) visual proofs by Dan Kalman from the March 1991 issue of The College Mathematics Journal (jstor.org/stable/2686447) and Martin Gardner from the October 1973 Scientific American (jstor.org/stable/24923225).

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

#math #manim #mathvideo #sumofsquares #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #finitesums #discretemath #induction #sumsumsquares #partialsums

Function Proof via Diagram Chasing (g composed f injective and f surjective implies g injective).

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