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:
Quasi-sphere hyperbolic plane, and its conjugate hyperbola, which is its counter-sphere. The "centre" of a quasi-sphere is a point that is equidistant from every point of the quasi-sphere – i.e., the quadratic form applied to the displacement vector (or radius vector) from the centre to a point of the quasi-sphere yields a constant, called the "radius squared", or equivalently, the point at which the pencil of lines normal to the tangent hyperplanes meet. If the quasi-sphere is a hyperplane, the centre is the point at infinity defined by this pencil. When , the displacement vector of the centre from the reference