A circle (blue) lies entirely in the plane; a horosphere (red) is tangent to the ideal circle, a hypercycle (purple) extends beyond the boundary of the plane, and a geodesic (green) is the hyperbolic-plane analog of a straight line.

When one point on the cycle is stereographically projected to the origin in the plane, the reciprocal of the Euclidean diameter can be used as an analog of the curvature of a Euclidean circle.