Pythagoras, Pythagorean Theorem, 3D Models, 勾股定理, ピタゴラス定理

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Pythagoras, Pythagorean Theorem, 3D Models The Pythagorean Theorem can be shown in action using 3D models. In reality, it's a straightforward outcome of a^2 + b^2 = c^2 in a 3D space. Pick any h > 0. Then, ha^2 + hb^2 = hc^2. We could build a box with a constant height along each side of the right triangle. But there's even more to it. We can construct countless 3D (or 2D) models. As long as the three 3D solids (or corresponding 2D shapes) are similar, the volume of the solid on the hypotenuse equals the sum of the volumes of the two solids on the two legs. Some 3D models look amazing; others aren't so impressive. Here are three 3D models on a right triangle that is 30mm, 50mm, and sqrt(3400)mm—semi-circle, square, and trapezoid. They all have a depth of 30mm. You can use water, sand, or rice to show the relationships. It's a bit messy but also fun for students!