Subject: More on Pythagorean triples
Date: Mon, 08 Dec 1997 07:30:53 +0000
From: Mohammed Sayeed
I've got a couple of problems which I hope you'll be able to solve for me.
I'm investigating pythagorean triples, and I have found a trend for the triples themselves, and thus have been able to form a general equation, i.e. a=2x+1, b=2x2+2x, and c=b+1.
Now, I sure this equation works, because I've tried it out and have come up with triples that adhere to a2 + b2 = c2. But I was wondering WHY c=b+1. Is it possible to have c=b+2, and if not why not? THAT is the first problem.
My second problem: Is there a general equation to express the relationship between a triple and its perimeter, i.e.
(3, 4, 5), P=12
(5, 12, 13), P=30
(7, 24, 25), P=56
(9, 40, 41), P=90
If there is an equation; is there also a proof for it?
Also is there a general equation to express the relationship between a triple and its area, i.e.
(3, 4, 5), A=6
(5, 12, 13), A=30
(7, 24, 25), A=84
(9, 40, 41), A=180
If there is an equation for this, is there a proof as well?