# horosphere

## English

The disk model of the hyperbolic plane, with a horosphere in blue.

### Etymology

A modern scientific coinage, probably from a Latinized spelling of Ancient Greek ὅρος (hóros, boundary) (not to be confused with ὧρος (hôros, year), which gave rise to many time-related terms) + sphere

### Noun

horosphere (plural horospheres)

1. An ${\displaystyle n-1}$ -dimensional hyperplane in hyperbolic ${\displaystyle n}$ -dimensional space: it is (in the Poincaré disk) Euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) Euclidean-parallel to the boundary hyperplane.