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
Circle of a sphere satisfy The intersection of the spheres is the set of points satisfying both equations. Subtracting the equations gives In the singular case formula_7, the spheres are concentric. There are two possibilities: if formula_8, the spheres coincide, and the intersection is the entire sphere; if formula_9, the spheres are disjoint and the intersection is empty. When "a" is nonzero, the intersection lies in a vertical plane with this x-coordinate, which may intersect both of the spheres, be tangent to both spheres, or external to both spheres. The result follows from the previous proof for sphere-plane intersections. Circle of a sphere A