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In hyperbolic geometry, an ideal point, omega point or point at infinity is a well defined point outside the hyperbolic plane or space. Given a line ''l'' and a point ''P'' not on ''l'', right- and left-limiting parallels to ''l'' through ''P'' converge to ''l'' at ''ideal points''. Unlike the projective case, ideal points form a boundary, not a submanifold. So, these lines do not ''intersect'' at an ideal point and such points, although well defined, do not belong to the hyperbolic space itself. The ideal points together form the Cayley absolute or boundary of a hyperbolic geometry. For instance, the unit circle forms the Cayley absolute of the Poincaré disk model and the Klein disk model. While the real line forms the Cayley absolute of the Poincaré half-plane model . Pasch's axiom and the exterior angle theorem still hold for an omega triangle, defined by two points in hyperbolic space and an omega point. ==Properties== * The hyperbolic distance between an ideal point and any other point or ideal point is infinite. * The centres of horocycles and horoballs are ideal points; two horocycles are concentric when they have the same centre. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ideal point」の詳細全文を読む スポンサード リンク
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