Books Received Published: 04 July 1907 Euclid's Parallel Postulate: its Nature, Validity, and Place in Geometrical Systems Nature 76, 220–221 (1907) Cite this article ...

The parallel postulate in Euclidean geometry states, for two dimensions, that given a line l and a point P not on l, there is exactly one line through P that does not intersect l, i.e., that is ...

The parallel postulate problem Around 300 BC, the Greek mathematician Euclid wrote a treatise on planar geometry called The Elements.

The parallel postulate was essential to Euclid in many of his proofs. But he could have chosen another axiom. For example, he could have started, as Thales did, with the sum of the angles of a ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don't apply: angles of a triangle add up to less than 180 degrees and Euclid's parallel postulate ...