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:
• Ten Epic Pythagorean P... (compilation)
• Pythagorean Theorem XI...
• Pythagorean Theorem I ...
• Pythagorean Theorem II...
• Pythagorean Theorem II...
• Pythagorean Theorem IV...
• Pythagorean Theorem V ...
• Pythagorean Theorem VI...
• Pythagorean Theorem VI...
• Pythagorean Theorem VI...
• Pythagorean Theorem X ...
or check out my Pythagorean theorem playlist:
• Pythagorean Theorem
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) : bookstore.ams..... 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 (studioinfinity..., 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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