Geometry of a Surface

Non-Euclidean Geometries

Lobachevskian/Bolyai Postulate

Given a line L and point P not on L

There are INFINITELY MANY lines through P parallel to L

Triangle Angle Sum < 180°

Riemannian Postulate

Given a line L and point P not on L

There are NO lines through P parallel to L

Triangle Angle Sum > 180°

Euclidean Parallel Postulate

Given a line L and point P not on L

There is exactly ONE line through P parallel to L

Triangle Angle Sum = 180°