On 7/15/07, Bill Gosper <gosper@alum.mit.edu> wrote: [snip]
WFL>This looks suspiciously like the area formula for the dual spherical polygon: this has angles and sides corresponding to the sides and angles of the of the original polygon (whose angles corrspond to dihedral angles, and sides to apical angles). See Todhunter.
Pending a jaunt to the Stanford Math Library, the formula says the
Todhunter Spherical Trig (an 1859 and an 1878 version) are both available as downloadable pdf files (about 2.5 and 3.5 megabytes) on line from google books: http://books.google.com/books?as_brr=1&q=Todhunter+Spherical&btnG=Search+Boo... (you may need a google id, now freely available for all, in order for the link to work) [snip]
Is someone out there who can say if Todhunter has the solid angle from vertex angles formula
cos(c) + cos(b) + cos(a) + 1 (d1) 2 acos ---------------------------- ? a b c 4 cos(-) cos(-) cos(-) 2 2 2
I didn't check .. but maybe someone will. [Odditum: and remainder deleted] Jim Buddenhagen