I am assuming that you have in mind a triangle mapped onto some form of curved or otherwise warped surface?

The presumption also is that the "straight line" is always the shortest distance along that surface and NOT through the intervening space?

I guess, if I understand this correctly, the simplest proposition would be a triangle of whatever size, mapped onto the surface of a sphere?

Mmm?  Is this where you are going? Maybe not, but ....

However, take a sphere, cut it into 8 via the 3 traditional axes [x,y,z].  Each 'triangle' has a vertex angle of 90º.  Cos(90º)= 0.

Equation?

......or am I treading dangerously?

Posted by brianjn on 2007-11-19 06:59:34