Euclidean geometry

Summary

Euclidean geometry is the geometry of the Euclidean plane and of Euclidean space: the study of points, lines, distances and angles in a flat space. It can be built synthetically from axioms, as in Euclid's Elements and Hilbert's axioms, or analytically with coordinates in $\R^n$. Its characteristic axiom is the parallel postulate; dropping it leads to absolute geometry and to non-Euclidean geometry.