Take a right triangle with integer sides A, B, & C.
(C need not be the hypotenuse.)

To side C attach another right triangle with integer sides C, D & E.

On this new triangle attach another right triangle to either side D or E.

Continue the process of attaching a new right triangle to the previous, creating a chain of integer right triangles.

No side length may be repeated.

If n is the number of triangles in the chain, what is the minimum largest side for n=2, 3, 4, 5, 6, 7, 8, 9, 10.

(In reply to n = 7 (Spoiler?) by Steve Herman)

a² + b² = c²

has too many solutions.

I wondered if there was an 'easy way' to compute Pythagorean triplets.

Google gave me an answer.

This does not give an answer to Jer's problem, but it gives a tool; the page can be saved to disk and there is documentation.

I did envisage using it to build chains of triangles.

From what I see of this java utility, Charlie either knows that such programs exist or that it offers complexities against  which his time resources do not allow.

Jer, Think this may be of value to you and your students:
http://www.faust.fr.bw.schule.de/mhb/pythagen.htm

This is a calculator.

Posted by brianjn on 2006-06-18 04:08:04