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 r with 0<r<π, there is a triangle in hyperbolic geometry whose angle sum in radians is equal to r.

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