hyperbolic geometry
"Hyperbolic geometry" is a form of non-Euclidean geometry that fundamentally alters the parallel postulate and has applications in fields like physics and cosmology.
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Definition
C2Mathematics
(technical, academic)A type of geometry where, given a line and a point not on it, multiple lines can pass through the point without intersecting the original line.
Example
- In hyperbolic geometry, the angles of a triangle add up to less than 180 degrees.
- Unlike Euclidean geometry, hyperbolic geometry allows for multiple parallel lines through a single point.
C2Mathematics
(technical, academic)A branch of geometry characterized by a space with constant negative curvature.
Example
- The surface of a saddle is an example of a shape with negative curvature, akin to hyperbolic geometry.
- Hyperbolic geometry is used to model certain aspects of the universe in cosmology.
Similar
Terms that have similar or relatively close meanings to "hyperbolic geometry":
conformal geometryspherical geometryfinite geometrycomplex geometrycontact geometrycombinatorial geometryaffine geometry