Ideal Point

In hyperbolic geometry, an ideal point, also called an omega point or a point at infinity, is a well-defined point that lies outside the hyperbolic plane or hyperbolic space itself, marking a direction in which geodesics converge rather than a point one can actually reach within the space. Ideal points appear in the standard models of hyperbolic geometry, where they typically sit on the boundary circle or boundary sphere that bounds the model, and they play a role analogous to points at infinity in other geometries. The same term is used differently outside geometry, most notably in political science, where an ideal point describes a position in a spatial model of voting, but that usage names a separate concept from the hyperbolic-geometry idea described here.