Re: Primitive Pythagorean Triples

Op 01/02/2025 om 11:02 schreef David Entwistle:

Hello,
 Are there any primitive Pythagorean triples where the one hypotenuse has
more than the two values for the other two sides? So, in the case of the
3, 4, 5 right triangle, there's the two possible arrangement of sides 3,
4, 5 and 4, 3, 5. Are there any triangles with more than two arrangements
for the one single size of hypotenuse?
 I haven't found any, looking at hypotenuse up to 10,000, but don't
immediately see why there couldn't be solutions of: a, b, h; b, a, h; c,
d, h and d, c, h.
 Apologies if this is inappropriate here. My maths is okay, but just high-
school level, nothing more...
 Thanks,

On the topic of Pythagorean triples, or perhaps slightly tangential,
I was just watching this interesting youtube video regarding points
in the plane that are not all co-linear at integer distances from one
another:
https://www.youtube.com/watch?v=fpIc-FE4c5U