Da Vinci’s Pythagorean Theorem Proof (Right triangle theorem) @MathVisualProofs

Uploaded March 2025 | Updated September 2026, 2 weeks ago

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

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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) : 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" : bookstore.ams.org/clrm-28.

For other proofs of this same fact check out:
youtu.be/q28H5NY5UVU
youtu.be/yfGtbNgcrQ8
youtu.be/JRjPsuJ7S-g
youtu.be/TsKTteGJpZU

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https://manim.community

Da Vinci’s Pythagorean Theorem Proof (Right triangle theorem)

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