The problem that starts this article: <https://www.cut-the-knot.org/triangle/pythpar/NonEuclid.shtml> is said to have a continuum of solutions but I was only able to find a denumerable set of them: the "obvious" one, starting at the North Pole and the ones near the South Pole where you go West on a parallel of length 10/n miles (you go around n times). Are there any other solutions?