Take it to the limit one more time – a history of calculus II

According to legend the Pythagoreans were devastated when they discovered that the diagonal of a unit square is an irrational number, because they believed that the natural numbers were the building bricks of the cosmos. It is even said that they murdered the man, who made the discovery. It wasn’t just the Pythagoreans, who had difficulties with the existence of irrational numbers or incommensurable numbers as the Greeks called them in their geometry. Taking our example of the diagonal of a square, one can’t measure it with a given fixed length. So, if the side of the square is 1 cm the diagonal cannot be measured by any rational multiple of 1 cm lengths. One can’t measure the one against the other. The mathematician whose was credited with supplying a solution to this problem was Eudoxus of Cnidus (c. 390–c. 340 BCE). He was born and died in Cnidus on the southwest coast of Anatolia. None of his original works have survived, although some fragments are preserved in the Commentaries…