What do Euclid, 12-year-old Einstein, and American President James Garfield have in common? They all came up with elegant proofs for the famous Pythagorean theorem, one of the most fundamental rules of geometry and the basis for practical applications like constructing stable buildings and triangulating GPS coordinates.

Named after Pythagoras, a Greek mathematician, the Pythagorean theorem tells us that the square (the result of multiplying a number by itself) of the longest side of the right triangle, the hypotenuse, is equal to the sum of the squares of the other two sides. See this demonstrated in different ways in this TED-Ed by Betty Fei, animated by Nick Hilditch: How many ways are there to prove the Pythagorean theorem?

Next, as seen in the vid above: The Pythagorean theorem water demo. Plus: The Brick Double-Domino Effect Explained and General relativity & why GPS wouldn’t work if we didn’t know about it.

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