# Pythagorean Proof

# Pythagorean Proof

This model physically demonstrates the Pythagorean Theorem. Any triangle that has a right angle between two of its sides will obey the rule that the sum of the squares of the two shorter sides equals the square of the longest side.

The area of a rectangle is equal to its height times its width, and for a square the height and width are the same, so the area of a square is equal to the length of one side multiplied by itself (hence the use of the term “squared” to mean a number multiplied by itself).

This model shows the relationship between the areas of three squares formed on the edges of a right triangle by allowing fine brass-plated steel beads to alternately fill up the one big square, or the two smaller squares. Because the area of the big square is, by the Pythagorean theorem, equal to the areas of the two smaller squares combined, the same number of beads fit exactly in both cases.