Circle of a sphere the Equator the only great circle. By contrast, all meridians of longitude, paired with their opposite meridian in the other hemisphere, form great circles. The diameter of the sphere which passes through the center of the circle is called its axis and the endpoints of this diameter are called its poles. A circle of a sphere can also be defined as the set of points at a given angular distance from a given pole. When the intersection of a sphere and a plane is not empty or a single point, it is a circle. This can be seen as follows:
N-sphere a central point, where the radius may be any positive real number. Thus, the -sphere would be defined by: In particular: An "n"-sphere embedded in an -dimensional Euclidean space is called a hypersphere. The -sphere of unit radius is called the unit -sphere, denoted , often referred to as "the" -sphere. When embedded as described, an -sphere is the surface or boundary of an -dimensional ball. For , the -spheres are the simply connected -dimensional manifolds of constant, positive curvature. The -spheres admit several other topological descriptions: for example, they can be constructed by gluing two -dimensional Euclidean spaces together,