Wikipedia
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.
Usage examples of "ideal point".
Our relationship, which I thought had reached its ideal point when we moved to Paris, was getting better and better.
In the past, the Minstrel Boy had found the Leader an ideal point at which to plug into the city's wealth of gossip and rumour.
If the Earth and the falling object were ideal point masses, with no length, no width, and no depth, then there are no other properties to speak of.
This slope will be the ideal point where we can begin to drive a shaft into the rocky ground, since neither of the space rockets can overlook what is going on here on the other side.
This works out quite well because it is an ideal point for transport.