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:
Exotic sphere Similar manifolds are called Brieskorn spheres. Given an (orientation-preserving) diffeomorphism , gluing the boundaries of two copies of the standard disk "D" together by "f" yields a manifold called a "twisted sphere" (with "twist" "f"). It is homotopy equivalent to the standard "n"-sphere because the gluing map is homotopic to the identity (being an orientation-preserving diffeomorphism, hence degree 1), but not in general diffeomorphic to the standard sphere. Setting formula_25 to be the group of twisted "n"-spheres (under connect sum), one obtains the exact sequence For , every exotic "n"-sphere is diffeomorphic to a twisted sphere, a result proven by