parallel postulate

noun

, Geometry.

1. the axiom in Euclidean geometry that only one line can be drawn through a given point so that the line is parallel to a given line that does not contain the point.

parallel postulate

1. See under Euclidean

Example Sentences

It can be shown that the parallel postulate refers to the geometry of two distinct types of surface, hinging on the phrase “at most one line”—which is mathspeak for “either one line or no lines.”

From Literature

Let’s return to the parallel postulate, which provides us with a very concise way of classifying flat, spherical and hyperbolic surfaces.

From Literature

The hyperbolic version of the parallel postulate states that for every straight line L and a point P not on that line, then there are an infinite number of straight lines parallel to L that pass through P. This is shown in the diagram below right, where I have marked three straight lines—L', L", and L'"—that pass through P but are all parallel to L. The lines L', L" and L'" are each parts of different circles that enter the disc at right angles.

From Literature

The parallel postulate provides us with a geometry for two types of surface: flat surfaces and spherical surfaces.

From Literature

One of the most determined aspirants in the quest to prove the parallel postulate from the first four postulates, and therefore show that it is not a postulate at all but a theorem, was János Bolyai, an engineering undergraduate from Transylvania.

From Literature