We discover suprising connections between three seemingly different problems:
finding right triangles with rational sides in a non-Euclidean geometry,
finding three integers such that the difference of the squares of any two is a
square, and the problem of finding rational points on an algebraic surface in
algebraic geometry. We will also reinterpret Euler's work on the second problem
with a modern point of view.Comment: 11 pages, 1 figur
