Date: Mon, 08 Dec 1997 07:30:53 +0000

From: Mohammed Sayeed

Hi,

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=2x^{2}+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 a^{2} + b^{2} = c^{2}. 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

etc.

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

etc.

If there is an equation for this, is there a proof as well?

Thanks loads,

Mohammed Sayeed

67102023