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:
Compute their product, then double it.
Square each, then subtract the two squares.
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.
Type your code here:
See your results here:
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?
Show a friend, family member, or teacher what you've done!
Here is a share link to your code:
Does your code work? Want to run it on your iPhone?
Here's your code:
Use [Control]-[C] (Windows) or [⌘]-[C] (MacOS) to copy your code.
Paste it using [Control]-[V] (Windows) or [⌘]-[V] (MacOS) into
Then click the "Use on iPhone" button that you'll see.