Pythagoras triples explained via central squares

Very much like today, the Old Babylonians (20th to 16th centuries BC) had the need to understand and use what is now called the Pythagoras' theorem x2 + y2 = z2. They applied it in very practical problems such as to determine how the height of a cane leaning against a wall changes with its inclination. This sounds trivial, but it was one of the most important problems studied at the time. A remarkable Old Babylonian clay tablet, commonly referred to as Plimpton 322 (Figure 1), was found to store combinations of three positive integers x, y, z that satisfy Pythagoras' theorem. Today we call them primitive Pythagorean triples where the term primitive implies that the side lengths share no common divisor.