Editing Euclidean space (section)

===Non-Euclidean geometries===
{{main|Non-Euclidean geometry}}
''Non-Euclidean geometry'' refers usually to geometrical spaces where the [[parallel postulate]] is false. They include [[elliptic geometry]], where the sum of the angles of a triangle is more than 180°, and [[hyperbolic geometry]], where this sum is less than 180°. Their introduction in the second half of 19th century, and the proof that their theory is [[consistency|consistent]] (if Euclidean geometry is not contradictory) is one of the paradoxes that are at the origin of the [[foundational crisis in mathematics]] of the beginning of 20th century, and motivated the systematization of [[axiomatic theory|axiomatic theories]] in mathematics.