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https://commons.wikimedia.org/wiki/File:Proofwithoutwords.svg
Image: Wikimedia Commons

A visual proof that the sum of all positive odd numbers up to 2n – 1 is a perfect square.

July 13, 2026July 12, 2026 | Science & Math

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Futility Closet is a collection of entertaining curiosities in history, literature, language, art, philosophy, and mathematics, designed to help you waste time as enjoyably as possible.

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