The other day I discovered one more way to derive Pythagoras’ equation from scratch, completely by accident. I was deriving Pythagoras’ equation using the usual method, whilst navigating a diagram similar to the one below, but without (B-A) measurements…

**Note (regarding diagram above): x+y = 90 degrees*

The usual method goes like this…

The area of the largest square is:

It is also:

Which means that:

Now, when I added the lengths (B-A) to my diagram, which are included in the diagram above, I discovered a new way to derive Pythagoras’ equation…

I did this by focusing on the area C^2. It turns out that:

And since:

I was able to say that:

Obviously, I was quite pleased. Have you discovered other ways in which to derive Pythagoras’ equation??

**Related:**

** Video** on how to come up with Pythagoras’s equation…