Helmut Richter wrote: >quasi wrote: > >> Conjecture (1): >> Conjecture (2): >> Conjecture (3): >> Conjecture (4): >> [...] > >That all your conjectures deal with cases n > 3 lets me suspect >that the case n = 3 is completely solved. I am afraid I do not >see that obvious solution. Perhaps I could learn something from >it for the other cases.
To generate rational triangles with circumradius 1, proceed as follows ...
Take any two rational right triangles with a leg length in common and glue them together along their common length leg so that the common length leg becomes an internal altitude of a new triangle. The new triangle will be a rational triangle with rational circumradius. Then rescale the new triangle to get a rational triangle with circumradius 1.
Moreover, the procedure outlined above generates _all_ possible rational triangles with circumradius 1.