# Lesson goal: Finding Pythagorean Triples

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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."

# Now you try. Try to translate the recipe for x, y, and z as stated above, and fill your results in for the x=, y= and z= lines.

For the x=, y= and z=, program in the formulas according to list items 1, 2, and 3 in the text above (i.e. let x be twice the produce of a and b). Run the code and generate your very own Pythagorean Triples! When you get your results, can you prove they satisfy the Pythagorean Theorem? Dismiss.
Show a friend, family member, or teacher what you've done!