>I am trying to figure out a math problem and I'm having trouble. I >wonder if anyone could give me a hint or an idea about how to go about >solving this question: Or, if someone knows where I could find a list >of a whole bunch of different pythagorean triangle combinations, I >know I would be able to figure it out. I'm just at a loss as to which >numbers I should try. > >Here's the question: > >Find four pythagorean triangles such that both pairs of the triangles >have the same areas. (all sides must be integers) > >Thank you.
Well, there are tables by A. Martin (Proceedings, Fifth International Mathematical Congress, Cambridge, 1912) which give all primitive solutions for which the hypotenuse does not exceed 3,000. However, it is useful to note that if (a,b,c) is a solution then so is (t*a, t*b, t*c). This may offer you a way out of your dilemna. Oh, there is also a general 'formula' for such triplets, but I would try the above multiplicative idea first.