model of hyperbolic geometry
C51335
concept
A model of hyperbolic geometry is a mathematical structure that represents the axioms and properties of hyperbolic space—where, unlike in Euclidean geometry, through any point not on a given line there exist infinitely many parallel lines—within a concrete setting such as the Poincaré disk or upper half-plane.
All labels observed (2)
| Label | Occurrences |
|---|---|
| metric of constant negative curvature | 1 |
| model of hyperbolic geometry canonical | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: model of hyperbolic geometry
Generated description
A model of hyperbolic geometry is a mathematical structure that represents the axioms and properties of hyperbolic space—where, unlike in Euclidean geometry, through any point not on a given line there exist infinitely many parallel lines—within a concrete setting such as the Poincaré disk or upper half-plane.
Instances (2)
| Instance | Via concept surface |
|---|---|
| Poincaré upper half-plane model | — |
| Poincaré metric | metric of constant negative curvature |