2c:T504,

Hyperbolic Geometry

A non-Euclidean geometry with the following property: Given a line m and a point P not on m, there are infinitely many lines passing through P which are parallel to m. Hyperbolic geometry may be thought of as plane geometry on a surface shaped like the bell of a trumpet.

A line m with arrows on both ends and a point P above it, not on the line.

See also

Elliptic geometry

2a:["$","main",null,{"children":["$","article",null,{"className":"SiteLayout-module__16F2PG__card","id":"mw-main","children":[["$","div",null,{"className":"SiteLayout-module__16F2PG__cardHead","children":["$","h1",null,{"className":"SiteLayout-module__16F2PG__cardTitle","children":"Hyperbolic Geometry"}]}],["$","div",null,{"className":"SiteLayout-module__16F2PG__content","children":[false,["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"DefinedTerm\",\"name\":\"Hyperbolic Geometry\",\"description\":\"Hyperbolic geometry is a non-Euclidean geometry where infinitely many lines through a point can be parallel to a given line. Explore its unique properties.\",\"url\":\"https://www.mathwords.com/h/hyperbolic_geometry.htm\",\"inDefinedTermSet\":{\"@type\":\"DefinedTermSet\",\"name\":\"Mathwords\",\"url\":\"https://www.mathwords.com/\"}}"}}],["$","div",null,{"className":"LegacyContent-module__gmcoNq__content ","dangerouslySetInnerHTML":{"__html":"$2c"}}],false]}]]}]}] 2b:["$","footer",null,{"className":"SiteFooter-module__C4mfIa__footer","children":["$","div",null,{"className":"SiteFooter-module__C4mfIa__inner","children":[["$","p",null,{"className":"SiteFooter-module__C4mfIa__title","children":"Mathwords: Terms and Formulas from Algebra I to Calculus"}],["$","p",null,{"className":"SiteFooter-module__C4mfIa__credit","children":["Written, illustrated by Bruce Simmons, and maintained by"," ",["$","a",null,{"href":"https://www.cazoommaths.com","target":"_blank","rel":"noopener noreferrer","children":"Cazoom Maths"}]]}],["$","p",null,{"className":"SiteFooter-module__C4mfIa__copyright","children":["Copyright © 2026 by"," ",["$","a",null,{"href":"https://www.cazoommaths.com","target":"_blank","rel":"noopener noreferrer","children":"Cazoom Maths"}],". All rights reserved."]}]]}]}]