Illuminating Hyperbolic Geometry

**I DO NOT OWN the copyrights for this video**

Original video - https://youtu.be/eGEQ_UuQtYs

Joint work with Saul Schleimer. In this short video we show how various models of hyperbolic geometry can be obtained from the hemisphere model via stereographic and orthogonal projection.

2D figure credits: 4:09 Cannon, Floyd, Kenyon, Parry. 0:49, 1:20, 1:31, 2:12, Roice Nelson. We thank Gazi University, Ankara, Turkey, for its hospitality during filming.

(2,3,7) triangle tiling: http://shpws.me/Dq6q
Geodesic saddle ({3,7} radius 3, subdivided 4): http://shpws.me/ES7b
Pseudosphere: http://shpws.me/GIgq
(2,3,5) triangle tiling (stereographic projection): http://shpws.me/CKVv

Wikipedia -
'In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all circular arcs contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.'