hyperbolic geometry

American  

noun

Geometry.

1. the branch of non-Euclidean geometry that replaces the parallel postulate of Euclidean geometry with the postulate that two distinct lines may be drawn parallel to a given line through a point not on the given line.

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Etymology

Origin of hyperbolic geometry

First recorded in 1870–75

Example Sentences

The project is a global community art initiative, produced mostly by thousands of women who crochet colorful, breathtakingly beautiful reef-like forms according to principles of hyperbolic geometry.

From Los Angeles Times • Aug. 29, 2024

With “Point of Infinity,” too, he says he’s interested in the play of presence and absence, or “the presence of immateriality” suggested by its hyperbolic geometry.

From New York Times • Jun. 9, 2023

Two main possibilities then arise: one is spherical geometry, in which parallel lines can eventually touch, in the way that Earth’s meridians cross at the poles; the other is hyperbolic geometry, in which they diverge.

From Nature • Mar. 20, 2017

Two initially parallel rays of light will diverge, and this is referred to as hyperbolic geometry.

From Textbooks • Oct. 13, 2016

Many of those properties of Euclidean parallels, which do not hold for Lobatchewsky’s parallels in hyperbolic geometry, do hold for Clifford’s parallels in elliptic geometry.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" by Various