Some of you know Pythagoras as the guy who correctly came up with the ratio of the sides of a right triangle. Now it's time you know him as a murderous cult leader. Maybe.

The dry, yet powerful Pythagorean Theorem haunts the minds of school children (and presidents), but Pythagoras was not the fusty old scholar that many make him out to be. To be sure, he was a math nerd. He loved numbers, and rationality. He just loved them a little too much. Around 500 BC, he founded a religion that came to be called Pythagoreanism. Pythagoras and his followers were sure that numbers explained everything in life, from nature to music. What's more, they were sure that everything in the universe was expressible as the result of rational numbers.

Rational numbers are numbers that can be expressed as the ratio of two whole numbers - in other words, as a fraction. If it wasn't expressible as x/y, they didn't want to hear about it. And I mean they *really* didn't want to hear about it.

Along, according to legend, came Hippasus. Hippasus was a Pythagorean, and he was an excellent mathematician. That didn't work out well for him. He noticed something about the pentagram. Namely that, if it's divided up, there is a certain ratio between the carved up pieces. Hippasus took the measure of the length of the red side divided by the green side. It's equal to the length of the green side divided by the blue side. And that's equal to the length of the blue side divided by the purple side. And none of these things are expressible as the ratio of two whole numbers. They form the golden ratio, which, in decimals, is approximately 1.61803.

The golden ratio shows up in many works of art and architecture. It forms the background aesthetic of our lives to this day. Hippasus was obviously clever, but not *that* clever. He announced that he'd found a way to demolish Pythagoras' religion on boat populated by only himself, Pythagoras, and a lot of other Pythagoreans for company. Legend has it that Pythagoras tipped him over the side, drowned him, and swore the rest of the group to secrecy.

It's doubtful this actually happened, especially since there's another rumor that Hippasus was killed not for coming up with the golden ratio, but with the square root of two - another irrational number. (He realized there was no rational way to express the diagonal of a square with sides one unit long.) Still, it makes you think twice before you sass your math teacher, doesn't it?

Via Magnificent Mistakes in Mathematics, UFL.

## DISCUSSION

The evidence for the golden Ratio (Phi) in Art and Architecture is circumstantial at best.

See Mario Livio's excellent book "The Golden Ratio".

He argues that people find the number in Art and Architecture because they want to find it - not because it is really there.