Sphere two poles is called the axis of rotation. Circles on the sphere that are parallel to the equator are lines of latitude. This terminology is also used for such approximately spheroidal astronomical bodies as the planet Earth (see geoid). Any plane that includes the center of a sphere divides it into two equal hemispheres. Any two intersecting planes that include the center of a sphere subdivide the sphere into four lunes or biangles, the vertices of which all coincide with the antipodal points lying on the line of intersection of the planes. The antipodal quotient of the sphere is the
Inversion in a sphere a powerful transformation. One simple example is in map projection. The usual projection of the North or South Pole is inversion from the Earth to a plane. If instead of making a pole the centre, we chose a city, then Inversion could produce a map where all the shortest routes (great circles) for flying from that city would appear as straight lines, which would simplify the flight path, for passengers at least. Let the reference sphere be Σ, with centre O and radius r denoted by {O, r}. All inverses, in this paper, are in the sphere Σ. The results