If one uses spherical geometry the angels in a triangle are bigger than 180° or pi.
This results form a violation of an axiom (from euclid). Unfortunately I don´t know which axiom is violated. My guess is that is the one that says "if a,b,c are different points on a straight line than one point lies between the other two points". Am I right? If not, which axiom of euclid is violated?

Question

If one uses spherical geometry the angels in a triangle are bigger than 180° or pi.
This results form a violation of an axiom (from euclid). Unfortunately I don´t know which axiom is violated. My guess is that is the one that says "if a,b,c are different points on a straight line than one point lies between the other two points". Am I right? If not, which axiom of euclid is violated?

phi · Answer

the parallel line postulate:   parallel lines never meet

phi · Answer

See http://en.wikipedia.org/wiki/Parallel_postulate

anonymous · Answer

So, you are saying that parallel lines do meet in spherical geometry?
I have trouble visualizing this.

phi · Answer

lines of longitude go straight north and south.  But they meet at the poles.

anonymous · Answer

I see. If these lines are called "straight lines" in spherical geometry I think I understand what you are saying.
Thank you, phi.

phi · Answer

If you define "straight line" to mean the shortest distance between 2 points (and you are required to stay on the surface of the sphere),  a "great circle"  e.g. longitudes or the equator is a straight line.  A great circle will form a circle whose center is the center of the sphere.