ideal triangle
In hyperbolic geometry, an ideal triangle is a set of three lines which connect three distinct points on the boundary of the model of hyperbolic geometry.
Below is an example of an ideal triangle in the Beltrami-Klein model:
Below is an example of an ideal triangle in the Poincaré disc model:
Below are some examples of ideal triangles in the upper half plane model:
speaking, none of these figures are triangles in hyperbolic geometry; however, ideal triangles are useful for proving that, given with , there is a triangle in hyperbolic geometry whose angle sum in radians is equal to .
| Title | ideal triangle |
|---|---|
| Canonical name | IdealTriangle |
| Date of creation | 2013-03-22 17:08:26 |
| Last modified on | 2013-03-22 17:08:26 |
| Owner | Wkbj79 (1863) |
| Last modified by | Wkbj79 (1863) |
| Numerical id | 5 |
| Author | Wkbj79 (1863) |
| Entry type | Definition |
| Classification | msc 51M10 |
| Classification | msc 51-00 |
| Related topic | LimitingTriangle |