Elliptic geometry

Summary

Elliptic geometry is the non-Euclidean geometry of constant positive curvature. In it, any two points determine exactly one line, and any two lines meet in exactly one point. Its standard model is the real projective space, seen as the sphere with antipodal points identified. There are no parallel lines, and the angle sum of a triangle exceeds $\pi$. Together with Euclidean and hyperbolic geometry it is one of the three classical geometries of constant curvature.