220px|right|thumb|A horosphere within the Poincaré disk model tangent to the edges of a [[hexagonal tiling cell of a hexagonal tiling honeycomb]] thumb|Apollonian sphere packing can be seen as showing horospheres that are tangent to an outer sphere of a [[Poincaré disk model]] In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of a sequence of increasing balls sharing (on one side) a tangent hyperplane and its point of tangency. For n = 2 a horosphere is called a horocycle.
220px|right|thumb|A horosphere within the Poincaré disk model tangent to the edges of a [[hexagonal tiling cell of a hexagonal tiling honeycomb]] thumb|Apollonian sphere packing can be seen as showing horospheres that are tangent to an outer sphere of a [[Poincaré disk model]] In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of a sequence of increasing balls sharing (on one side) a tangent hyperplane and its point of tangency. For n = 2 a horosphere is called a horocycle.
A horosphere can also be described as the limit of the hyperspheres that share a tangent hyperplane at a given point, as their radii go towards infinity. In Euclidean geometry, such a "hypersphere of infinite radius" would be a hyperplane, but in hyperbolic geometry it is a horosphere (a curved surface).
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).