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

The project also explores mathematical themes, since many living reef organisms biologically approximate the quirky curvature of hyperbolic geometry.

From New York Times • Jan. 15, 2024

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

From Textbooks • Oct. 13, 2016

Broadly, Farris starts with symmetries of curves, moves to symmetries in the Euclidean plane, and ends by exploring analogous symmetries in spherical and hyperbolic geometry.

From Scientific American • Sep. 14, 2015

From these and a few other remarks it appears that Gauss possessed the foundations of hyperbolic geometry, which he was probably the first to regard as perhaps true.

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