A Visual Proof of the Pythagorean Theorem
Автор: Richard Behiel
Загружено: 2020-12-08
Просмотров: 5097
Описание:
Here we have two big square geometric patterns. On the left side of the screen, there are four triangles arranged as adjacent pairs. On the right side of the screen, there are four triangles arranged in a different way.
Because both arrangements have the same total area (left big square = right big square), and both arrangements have four identical triangles, the area in each arrangement which isn't triangles must be equal. On the left side, this area is the sum of a^2 and b^2. On the right side, this area is c^2. Therefore, a^2 + b^2 = c^2.
This proof works for all right triangles. Any a/b ratio fits in this square diagram, so the concept holds regardless of the shape of the right triangle. Since the overall size of these diagrams doesn't matter, the proof is true for triangles of any size. Any shape, any size = for any right triangle, must be true that a^2 + b^2 = c^2.
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