horosphere

Meaning

Noun

• An $n-1$-dimensional hyperplane in hyperbolic $n$-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.

Origin

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