This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) following essentially Euclid's proof. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. As a bonus, we show how to use Euclid's shear and rotate proof to create a dissection proof of the Pythagorean theorem. Which of these proofs do you prefer?

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For other proofs of this same fact check out:
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or check out my Pythagorean theorem playlist:

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This animation is based on a proof due to Euclid. For a static version of this proof, see Roger Nelsen's first "Proof Without Words: Exercises in Visual Thinking" compendium (page 5) : [ Ссылка ]. You can also check out Howard Eves' "Great Moments in Mathematics (Before 1650)" page 31-33.

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The dissection proof was suggested to me by Glen Whitney ([ Ссылка ]), and Glen then found a similar dissection in the compendium of Pythagorean theorem proofs from Elisha Loomis (Proof 21 on p. 122 ).
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#math #pythagoreantheorem #pythagorean #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo

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