# A Pythagorean Pun

There were once 3 kingdoms that bordered the same lake. In the middle of the lake there was an island, and the 3 kingdoms had been fighting over it for years. No one seemed to be able to keep the upper hand for very long and no one had been victorious. The wars over this little island were very costly, but all 3 kingdoms wanted it because of its great beauty and resources.

Finally, the monarchs agreed to a way to settle the matter permanently. Each would send their knights and squires to the island and they would
fight it out. Whoever’s knights and squires won the day would keep the island forever.

One kingdom sent many knights and each knight had a few squires. The night before the battle, the knights polished their armor while the squires readied the weapons. When the armor was finished, the knights sat around the fire drinking.

The second kingdom sent more knights than the first and each knight had several squires. The night before the battle, the knights drank around the fire while the squires scurried about polishing armor and readying weapons.

The third kingdom only sent one knight and he had only one squire. While the squire polished armor and readied the weapons, the knight hung a single pot from the tallest branch of the tree and tied a rope with a loop at the end from another branch. Then the knight sat by the fire and drank while the squire kept working.

The fateful day came and all the squires came out to the battlefield. (The knights had stayed up too long drinking.) The battle was fierce. In the
end, only the lone squire from the third kingdom was left standing. Proving once again, the age old theorem:

The squire of the high pot and noose is equal to the sum of the squires of the other two sides.

The punch line of this joke is a pun on the Pythagorean Theorem, often stated as: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. You may recall from our venture into trigonometry humor that a right triangle has one ninety-degree angle, and that the hypotenuse is the side opposite the right angle (also the longest side in the triangle).

Never argue with this triangle; it is always right.

The Pythagorean Theorem (named after Pythagoras of Samos, but known to people long before his time) states a curious relationship between the lengths of the sides of a right triangle. Imagine extruding the sides of a right triangle outward to form three squares, like this:

According to the Pythagorean Theorem, the area of the square formed from the hypotenuse is equal to the combined areas of the other two squares. In other words, if you could dismantle the squares formed from sides a and b and recombine them into one square, it would be the same size as the square formed from side c.

Mathematically, the Pythagorean Theorem can be expressed as a2 + b2 = c2. It holds true for any right triangle (as long as the triangle is flat; it doesn’t work for triangles printed on curved surfaces). Here’s an animation demonstrating how the Theorem works, courtesy of Wikipedia.

Now about that joke: I dig the pun at the end, but number-wise, it doesn’t quite work. If the third kingdom represents the hypotenuse (or high pot and noose), it should be the largest force of the three kingdoms. Assuming the first kingdom had, say, 300 squires and the second kingdom had 400 squires, the third kingdom would need 500 squires to be their equal, Pythagorealistically speaking. 3002 + 4002 = 5002. I know, I know…it’s just a stupid pun, but I want this blog to be an avenue for learning as well as laughing, so I would be remiss not to mention it.