Most people have heard of the Pythagorean Theorem, which states that $c^2=a^2+b^2$, where $c$ is the hypotenuse of a right triangle, and $a$ and $b$ are the other two sides (or legs) of the right triangle.

Quick! Could you guess three numbers that satsify $c^2=a^2+b^2$? You might have the famous 3-4-5 right triangle memorized.

Here is a quick computer way of generating numbers that satisfy Pythagorean's Theorem. Or stated another way, numbers that would work just fine as side lengths for a right triangle.

Here's the way it works. Start by thinking of any two numbers. Then do three calculations with them:

1. Compute their product, then double it.
2. Square each, then subtract the two squares.
3. Square each, then sum them.

The three results you get are sides that would form a correct right triangle! These three steps are called"Diophantus's Rules."

print("What is the larger of your numbers?")

a=input()

print("What is the smaller of your numbers?")

b=input()

​

x=???

y=???

z=???

​

print("A triangle with side lengths of")

print(x,",",y,"and",z,"would form a right triangle")