Pythagorean Theorem V (visual proof; Leonardo da Vinci)

This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the a diagram that is now attributed to Leonardo da Vinci. The proof uses reflection and rotation symmetry arguments. 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. #mathshorts #mathvideo #math #pythagoreantheorem #pythagorean #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #leonardodavinci #davinci


01:30 I said something incorrect so made a small cut. I meant to say the two hexagons are made from congruent parts.

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This animation is based on a proof due to Leonardo da Vinci. For a static version of this proof, see Roger Nelsen's first "Proof Without Words II: More Exercises in Visual Thinking" compendium (page 5) : https://bookstore.ams.org/clrm-14/. You can also check out Howard Eves' "Great Moments in Mathematics (Before 1650)" page 29--31 and Roger Nelsen's book "Math Made Visual: Creating Images for Understanding Mathematics" : https://bookstore.ams.org/clrm-28.

For other proofs of this same fact check out:
   • Pythagorean Theorem I (visual proof)  
   • Pythagorean Theorem II (visual proof)  
   • Pythagorean Theorem III (visual proof)  
   • Pythagorean Theorem IV (visual proof;...  

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Music in this video:
Tranquil Fields (Tense) by Alexander Nakarada | https://www.serpentsoundstudios.com
Music promoted by https://www.free-stock-music.com
Attribution 4.0 International (CC BY 4.0)
https://creativecommons.org/licenses/...