From: Lynn Killingbeck Subject: Re: Simple geometry problem Date: Tue, 19 Sep 2000 17:28:38 -0500 Newsgroups: sci.math Summary: [missing] Jeremy Boden wrote: > > In article <8pvvbb$orb$1@nnrp1.deja.com>, kgeorgie@hotmail.com writes > >Help! > > > > What is the maximum number of degrees in a triangle in spherical > >space??? > > > From: "Aron Santi" <@tin.it> > > A triangle is a bidimensional geometrical object... so the angle sum > will be > always 180 degrees. > But if you refer about solid angol.... well its max is 4*pi... > > --------------------------------------------- > > It would help if your newsreader could quote an extract of the post you > are replying to. > > Anyway, a spherical triangle is not "bidimensional" (2-dimensional ???). > It's a surface in 3 dimensions. > > A spherical triangle which has 3 right angles is easily constructed > (angle sum = 270 degrees):- on the Earth (supposedly a sphere) simply > take any octant. > > I'm sure you could achieve an angle sum of 360 degrees on a sphere > though - possibly more. > > -- > Jeremy Boden "Proposition XIX. Theorem 431. The sum of the angles of a spherical triangle is greater than 180 degrees, and less than 540 degrees." From my ancient solid geometry book copyright 1950, by Smith and Marino. Even ends with a Q.E.D., so there is no way it could be wrong! Lynn Killingbeck ============================================================================== From: israel@math.ubc.ca (Robert Israel) Subject: Re: Simple geometry problem Date: 19 Sep 2000 19:10:28 GMT Newsgroups: sci.math In article <8pvvbb$orb$1@nnrp1.deja.com>, wrote: > What is the maximum number of degrees in a triangle in spherical >space??? Do you mean the maximum sum of angles in a spherical triangle? That would be 900 (not really maximum, but supremum: take the "outside" of an arbitrarily small triangle). Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2