Pythagorean Proof

This is a physical demonstration of the pythagorean theorem, which states that, for any triangle that has a right angle between two of its sides, the square of the length of the longest side is equal to the sum of the squares of the other two sides.

In mathematics “square” means multiplying a number by itself, so if the lengths of the sides are a, b, and c, the pythagorean theorem says that a×a + b×b = c×c, which is more commonly written as a2 + b2 = c2. Now, there is a very good reason why this operation is called “squaring”...it's because the area of a square is equal to the length of one of its side multiplied by itself. So if you attach a square to one side of a triangle, the area of that square will be equal to the “square” of length of that side.

This model is filled with quite beautiful gold-colored 0.8mm diameter (super-small) metal beads that can flow back and forth between the literal squares on each side of the triangle. There are just enough beads to fill the largest square, and because of the Pythagorean theorem, this number of beads is necessarily also exactly the right amount to fill the two smaller squares. By tipping the model in different directions, you can see this equivalence in action.

In this orientation we see that there are just enough beads to fill an area of c^2 (c times c).

In this orientation we see that the same number of beads also exactly fill the sum of the areas of a^2 plus b^2.

Your model will arrive attractively packaged with all the necessary parts (even a screwdriver). The kit screws together in about 15 minutes, and does not require any special model-building skills. A detailed, step-by-step assembly video is available on our instructions page.