View source for Horosphere

''orisphere''

A surface in Lobachevskii space, orthogonal to (hyperbolic) parallel straight lines in a certain direction. A horosphere can be considered as a sphere with centre at infinity. A Euclidean geometry can be realized on a horosphere if straight lines are taken to be horocycles (cf. [[Horocycle|Horocycle]]), the order of the points is defined through the order of the straight lines in the pencil of parallels defining the horocycle, and a motion is taken to be a motion in Lobachevskii space that takes the horosphere onto itself.



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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  H.S.M. Coxeter,   "Introduction to geometry" , Wiley  (1961)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  A.P. Norden,   "Elementare Einführung in die Lobatschewskische Geometrie" , Deutsch. Verlag Wissenschaft.  (1958)  (Translated from Russian)</TD></TR></table>