The Legend of Pythagoras

Some mathematically-inclined friends were having a boat trip. There was all sorts of food, drink, and numerical merriment aboard the S.S. Pythagoras. That is, until one of them brought up a proof he had recently been working on.

"Friends, there DOES exist a number that is not rational. I have come up with a most ingenious proof of this!" said Julius.

"WHAT?" exclaimed the rest of the group.

"Indeed! You see, if you draw a triangle, such that one of its angles is ninety-degrees, and such that the two incident sides to the right angle are each of length one, then the hypotenuse's length is irrational. It would be equivalent to the square root of the number two, but that number cannot be written as one integer divided by another. One or both numbers would have to be..."

But it was at this point that the group of friends, led by the famous Pythagoras of Samos, declared poor Julius a heretic and threw him overboard. The night air was immediately rent with his screams and pleas for help, and the laughter and singing and celebrations of the rest of the group as they sailed away. For a great mathematical secret died that night with Julius as he drowned, and was not discovered again until a great number of years later. He had, in fact, been correct--the square root of two, as well as many other numbers, are irrational, and cannot be written as one integer divided by another.