In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate. A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry. Geometry that is independent of Euclid's fifth postulate (i.e., only assumes the modern equivalent of the first four postulates) is known as absolute geometry (or, in other places known as neutral geometry).
Read more about Parallel Postulate: Equivalent Properties, History, Converse of Euclid's Parallel Postulate, Criticism
Famous quotes containing the word parallel:
“As I look at the human story I see two stories. They run parallel and never meet. One is of people who live, as they can or must, the events that arrive; the other is of people who live, as they intend, the events they create.”
—Margaret Anderson (1886–1973)