Pythagorean Therom Proof

thingiverse

This is a straightforward manipulative that clearly demonstrates how the Pythagorean Theorem can be verified using rearrangement techniques. We start with a tray featuring a fixed internal area of (a+b)^2 and four identical triangles with side lengths a, b, and c. By arranging these triangles around the perimeter of the tray as depicted in figure one, we reveal that the negative space within is shaped like a square measuring c units on each side. In a second step, by rearranging the triangles to form rectangles, as shown in figure two, the remaining negative space gets split between two squares, one measuring a units and another measuring b units. Given that the unoccupied space remains unchanged, we arrive at a2 + b2 = c2, proving the Pythagorean Theorem's validity through this intuitive and compelling visual representation. This design was created using Tinkercad.