In elementary arithmetic geometry, stereographic projection from the unit circle provides a means to describe all primitive Pythagorean triples.  Specifically, stereographic projection from the north pole (0,1) onto the -axis gives a one-to-one correspondence between the rational number points  on the unit circle (with ) and the rational points of the -axis.  If  is a rational point on the -axis, then its inverse stereographic projection is the point
which gives Euclid's formula for a Pythagorean triple.