Re: spherical geometry

[John Denker <jsd@AV8N.COM>]

Ludwik Kowalski wrote:
> 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?

Sorry, not correct.  Consider the benchmark case of the
90-90-90 triangle.  The planes are mutually perpendicular.

AFAIK the only way you can recover 60 degree angles is
to draw the _chords_ between the corners of the spherical
triangle.  These chords form an ordinary flat equilateral
triangle in the interior of the sphere.  I make no guarantee
that these interior constructs are helpful or interesting,
but they do exist.

BTW you don't need the scare-quotes around "triangle".
Great circles are geodesically straight in a spherical
world.  So we can properly speak of a spherical triangle;
it is not a misnomer.