# Pythagoras has a posse

Let’s talk about Pythagoras for a moment, shall we? Everyone learns his theorem in school – the square of the hypotenuse is the sum of the squares of the other two sides. So if you take the length of one side of a right-angled triangle, and square it; then take the length of the next side, and square it; add up those two numbers and it will equal, as if by magic, the length of the hypotenuse (the long side of the triangle), squared.

3 squared + 4 squared = 5 squared

It’s a beautiful thing.

And as any pulp novel will tell you, people kill for beautiful things all the time.

Pythagoras did more than just do maths. He believed in it. He believed that numbers held a mythical power. He had a whole cosmology of beliefs all around numbers and the power they have. In his system the number 1 was  connected to reason, 2 was opinion and diversity, 3 was harmony, and 4 – well, I’ll let you listen to the podcast for that one. He was the first person to divide numbers up into ‘odd’ and ‘even’ – but he went further than taxonomy, and said odd numbers were masculine and even numbers were feminine.

By the time he was in his fifties he had a following… a less charitable soul might call it a cult. His followers even built up a mythos around their leader – that he had a golden thigh, that he had come back from the dead, that he was the son of the god Apollo, that his mother was a virgin (sound familiar?) (well, maybe not the golden thigh thing). The Pythagoreans worshipped whole numbers and fractions, believing them to be the basis for the universe.

The problem came when you have a unit square. It’s one unit – centimetres, metres, feet, whatever – long and one unit high. A simple question is then: what is the length of the diagonal? Well, handily, we can use the Pythagorean Theorem for that. Cut the square into two triangles, so that the hypotenuse of each triangle is that diagonal, and you end up with a right-angled triangle that is one unit high and one unit long. Do the maths, and you discover that the length of the diagonal is the square root of 2. Simple.

But not if you believe that the entire universe is made up of whole numbers and fractions. The square root of two is irrational – that is, it goes on forever. It can’t be described as a fraction. So Pythagoras did what any sensible religious leader does when they’re faced with something which directly contradicts a central tenet of their faith. He banned his followers from talking about it on pain of death.

And that was no idle decree. A young Pythagorean named Hippasus revealed the paradox – and he was assassinated.

Some people kill for money, some for love, some just for the fun – but Pythagoras was the first person to kill for maths.

Much of the information for this post came from Leonard Mlodinow’s wonderful book ‘Euclid’s Window’