As Sharon has alluded to in her question (diameter or circumference) Nigel's formula to come to all other solutions is strictly speaking wrong (though correct for all practical purposes). His formular comes from the planar geometry and the correct formula (which I don't know) would have to come from spherical geometry.

The 'error' he makes is to treat the earth as if it was flat. Since we all know that this error (centimetres?, millimeters?)is very small for walks of up to two miles and certainly smaller than any random deviation in our walking, for all practical purposes Nigel has given all possible solutions for all practical purposes .

Wolfgang