horosphere

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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 -dimensional hyperplane in hyperbolic -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.

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