# Hyperbolic Geometry & Conformal Maps

## Möbius Transformations

Some notes about Möbius transformations, which are especially nice conformal maps. Well, in 2D they're especially nice. In higher dimensions all conformal maps are Möbius transformations!

## Milnor's Lobachevsky Function

Milnor's Lobachevsky function is a strange, and strangely named, function which is surprisingly useful for discrete uniformization.

## Penner Coordinates

Although ideal hyperbolic triangles have infinite perimeters, we can still assign them meaningful numbers that act like side lengths. These are called

*Penner coordinates*.## Discrete Conformal Maps and Ptolemy Flips

Notes exploring the connections between discrete conformal maps, circumcircle-preserving projective maps, and Ptolemy flips, as described in Discrete Conformal Maps and Ideal Hyperbolic Polyhedra by Bobenko, Pinkall and Springborn and Ideal Polyhedra and Discrete Uniformization by Springborn.