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
N-sphere then is uniformly distributed within the unit -ball (i.e., by simply discarding two coordinates). Note that if is sufficiently large, most of the volume of the -ball will be contained in the region very close to its surface, so a point selected from that volume will also probably be close to the surface. This is one of the phenomena leading to the so-called curse of dimensionality that arises in some numerical and other applications. N-sphere In mathematics, the -sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension. It is an -dimensional manifold that can be embedded