It was a dismally sunny day in the kingdom of Mathematicals. It was also the day when King Euclid had a very terrible problem.
“My palace is in desperate need of a new coat of paint,” he said, “but I have no idea how much to buy!” Euclid’s palace was shaped like a triangle, and while the width and the height of it were commonly known (indeed, printed every year in the Mathematical Almanac), nobody knew the length of the hypotenuse.
So throughout the entire kingdom everyone cobbled together all their rulers and tape measures and marched to the palace.
Unfortunately, numbers are very clumsy things, having no opposable thumbs, and the day was so rife with people dropping their rulers and letting their tape measures go floppy it was impossible to get a reading. When the sun went down, everyone was forced to admit their failure.
“Why this dismal failure?” said King Euclid. “I demand to know the problem!”
The jesters Inch and Centimeter, who were in charge of the project, bowed low and said:
“The rulers were dropped and the tape measures were floppy, sir. Besides, no one could decide if we were measuring in metric or not.”
The king slapped his forehead and pronounced them knaves.
“Knaves!” he pronounced, slapping his forehead. “Is there no one who knows the measurement of the hypotenuse?”
“Well,” began Inch.
“There is one,” said Centimeter. “He lives somewhere in the city. He’s a hermit. Nobody likes him very much. But his wisdom is renowned through all the land.”
“Bring him here!” said Euclid, “before I have you two beheaded!” And so Inch and Centimeter hurried out into the city to find the wise old man.
First they looked down Algebra street. They saw vendors selling Xs and Ys, and the city’s Cartesian playing field, where some small numbers were playing with some imaginary numbers, and rows upon rows of simultaneous buildings.
“I see many things related to algebra,” said Inch, “but I do not see a wise old man.” So they went on and looked down Trigonometry Lane. There they saw vendors selling ? and large posters advertising the food unit circle.
“I see many things related to Trigonometry,” said Centimeter, “but nothing remotely geriatric.” So they went on and looked down Geometry Boulevard, where they saw him. A very old man in a toga stood in the center of the street. On his head he wore an enormous hat with “Pythagoras” emblazoned across it.
Inch and Centimeter rushed to him and grasped his hands.
“Are you the wise old man?” cried Inch.
“Are you the hermit nobody likes very much?” cried Centimeter.
“Unhand me, thou dogs!” spake Pythagoras, casting them asunder.
“The king has a problem!” said Inch.
“We need you!” said Centimeter.
“Forsooth!” spake Pythagoras. “Thou art fools! I am a hermit, and such folk do not mix with thine own, nary, not even for a king!”
Inch and Centimeter exchanged very confused glances.
“I think that means he’ll do it,” said Centimeter, so they dragged Pythagoras off to the palace.
Grumpily, the wise hermit spake:
“Hark, yonder side A is 3 lengths from one end to the other, and yonder side B is square root of 7 lengths from one end to the other. The squares of yonder A and B, put together in such a manner to make a sum, will equate the square of the wall beseeching paint.”
This speech confused everyone. The courtiers threw their hands up in despair, the attendants ran in hopeless circles, and the pages ran in hopeless circles with their hands thrown up in despair.
“Enough!” roared King Euclid. “You are a very annoying old man and I have little patience for togas. If you don’t tell me how much paint I need this instant, I will have you beheaded!”
Pythagoras glared sulkily.
“3 lengths of paint,” he spake, and immediately there was much rejoicing, and three lengths of paint was purchased, and the wall was painted.
However, once the last stroke was struck, something was terribly wrong.
“The wall is nowhere near complete!” roared Euclid. “Have Pythagoras beheaded at once!” So the old man was dragged off and rounded to the nearest tenth.
And for the rest of the history of the kingdom of Mathematicals, one great spot on the hypotenuse of the palace was unpainted, until the savages of Non-Euclidian Geometry invaded and burned the palace to the ground.
Moral: Always double-check your answers.