parallel postulate


parallel postulate

One of the five postulates, or axioms, of Euclid underpinning Euclidean geometry. It states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. Unlike Euclid's other four postulates, it never seemed entirely self-evident, as attested by efforts to prove it through the centuries. The uniqueness of Euclidean geometry, and the absolute identification of mathematics with reality, was broken in the 19th century when Nikolay Lobachevsky and János Bolyai (1802–60) independently discovered that altering the parallel postulate resulted in perfectly consistent non-Euclidean geometries.

This entry comes from Encyclopædia Britannica Concise.
For the full entry on parallel postulate, visit Britannica.com.

Seen & Heard

What made you look up parallel postulate? Please tell us what you were reading, watching or discussing that led you here.

Get Our Free Apps
Voice Search, Favorites,
Word of the Day, and More
Join Us on FB & Twitter
Get the Word of the Day and More