Dan, Yes, your central angle theorem is the same as my central angle theorem; I was reformulating it in a non-standard (and, I now see, confusing) way that I thought would be likely to generalize. Maybe I should just ask the question of whether there's ANY formulation of the central angle theorem that extends to solid angles... Jim On Thursday, December 31, 2015, Dan Asimov <asimov@msri.org> wrote:
On Dec 30, 2015, at 8:56 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
The central angle theorem (in one formulation) tells us that if C is a circle containing the point p and C' is a circle centered at p, then projection from C to C' through p halves all angles.
For some reason I'm having trouble imagining this projection properly.
Is this "central angle theorem" the same as the theorem that says:
An angle inscribed in a circle subtends a central angle that's twice its size
?
—Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun