Fix two points in a Euclidean plane, and stereographically project a spherical globe to the plane so that the poles map to our chosen points. The family of circles passing through both points corresponds to the family of longitudes on the globe. Curves that at each point are orthogonal to these circles turn out also to be circles, corresponding to the family of latitudes on the globe. Collectively, the two families are sometimes known as "Apollonian circles" after Apollonius of Perga.
