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# Re: spherical geometry

Each angle, of the equilateral "triangle" defined by Carl, is slightly
larger than 60 degrees. But the angles between the planes containing
the edges (containing three great circles) are always 60 degrees. Is
this correct?

On Thursday, Aug 19, 2004, at 11:12 America/New_York, Ludwik Kowalski
wrote:

I am trying to address Carl's problem in my own way but I need help.

Consider a point A located on a sphere of unit radius. The polar
axis of the sphere, z on my picture, is vertical. The two spherical
coordinates of A are TET (polar angle) and PHI (azimuthal angle).

Another polar axis, z', is chosen. Its orientation, in the old frame,
is specified by ALPHA (polar) and BETA (azimuthal). How are new
polar coordinates, TET' and PHI', expressed in terms of old polar
coordinates? I realize that the transformation is not as simple as
for xy and x'y'.

Ludwik Kowalski