hyperbolic geometry (Meaning)
hyperbolic geometry (n)
(mathematics) a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane
Synonyms & Antonyms of hyperbolic geometry
No Synonyms and anytonyms found
hyperbolic geometry Sentence Examples
- Hyperbolic geometry, a non-Euclidean geometry, challenges the notion of parallel lines.
- In hyperbolic geometry, the sum of the interior angles of a triangle is less than 180 degrees.
- The famous Escher drawing "Circle Limit IV" exemplifies the paradoxical nature of hyperbolic geometry.
- Hyperbolic surfaces have a negative curvature, which gives them saddle-like shapes.
- The Poincaré disk model and the Klein disk model are two common models used to visualize hyperbolic geometry.
- Hyperbolic geometry finds applications in architecture, art, and theoretical physics.
- The Lobachevsky plane is a fundamental example of hyperbolic geometry with constant negative curvature.
- Hyperbolic knots are knots that are tied in hyperbolic 3-space and exhibit unique properties.
- The Gauss-Bonnet theorem provides a useful tool for understanding the geometry of hyperbolic surfaces.
- Hyperbolic geometry has influenced the development of modern mathematics and theoretical models in various fields.
FAQs About the word hyperbolic geometry
(mathematics) a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines t
No synonyms found.
No antonyms found.
Hyperbolic geometry, a non-Euclidean geometry, challenges the notion of parallel lines.
In hyperbolic geometry, the sum of the interior angles of a triangle is less than 180 degrees.
The famous Escher drawing "Circle Limit IV" exemplifies the paradoxical nature of hyperbolic geometry.
Hyperbolic surfaces have a negative curvature, which gives them saddle-like shapes.
