Pythagoras on Hinges, Dissection Models for the Pythagorean Theorem

There are numerous ways to prove the Pythagorean Theorem! And there are also many ways to make sense of the squares on the three sides of a right triangle using dissections. In the present design, I used a classic dissection, where the square on the longer leg is dissected into four congruent quadrilaterals and further hinged with the square on the short leg. Hence, we have a string of five (3D) shapes, which can be folded into the square (box) on the hypotenuse, or the two squares (boxes) on the two legs. The pictures speak for the transformation. Of course, the height of the model does not count with the Pythagorean Theorem. Nonetheless, since the pieces all have the same height in a specific model, the volumes of the three boxes (outer) also follow the Pythagorean Theorem.

To use the dissection model, one needs to print at least one set of the five-piece file, leaving the right triangle to the imagination. If so desired, one can use two copies of the five-piece file plus the corresponding right triangle. Of course, the five-piece structure also behaves like a puzzle—one square to/from two squares. Have fun!

Among the files

1. Five-piece structure in two sizes (25-50-hypotenuse, 40-100- hypotenuse)
2. Right triangle in two sizes (25-50-hypotenuse, 40-100- hypotenuse)

References

1. https://www.cut-the-knot.org/pythagoras/
2. https://www.cs.purdue.edu/homes/gnf/book.html