Comments by "David Terr" (@dcterr1) on "Визуализация теоремы Пифагора: лучшие доказательства и неожиданные повороты" video.

Fanstastic video! It's amazing to see how beautiful and versatile the Pythagorean theorem is and how many generalizations it allows. One could even make the case that the Pythagorean theorem was in a sense the foundation for mathematics! I just think it's unfortunate that Pythagoras got too much credit for it, since he probably wasn't the first to prove it, but I guess that's how history goes.
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@Achill101 Watch from 10:30 to 11:37. This is essentially the same proof Einstein came up with.
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Is anyone here familiar with Einstein's proof, which he came up with when he was just 12? It involves adding the areas of the two triangles obtained by dissecting the original right triangle into two smaller similar right triangles.
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@Achill101 Einstein gave a proof at age 12 involving similar triangles. I think it's referred to in this video. Divide the right triangle into two similar right triangles and consider the areas of each subtraingle as well as the original right triangle. Since these areas add and the hypotenuses of each triangle correspond to the three triangles, and since area is proportional to the square of the hypotenuse, we have a² + b² = c². Pretty neat, huh?
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