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 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