Pythagoras' Theorem Part 3

In the previous post, I mentioned that the
numbers obtained, a, b and c, would satisfy
the equation a² + b² = c².

I want to prove that in this post. Firstly,
I want to show the algebraic form of the
numbers, which we obtained in the previous
post:

a= a
b= ( a²-1 ) / 2
c= ( a²-1 ) / 2 + 1.

So plugging these into the equation you get
the following results:

I couldn't be bothered to type out all the HTML
code needed to write all the expressions, so I put
it down on paper, and then scanned it. I then sent
an e-mail to myself and there you have it.

I hope you enjoyed all the Pythagoras' Theorem
posts, and feel free to point out any mistakes in
the maths, if you find any.