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:
Sphere spectrum Sphere spectrum In stable homotopy theory, a branch of mathematics, the sphere spectrum "S" is the initial object in the category of spectra. It is the suspension spectrum of "S", i.e., a set of two points. Explicitly, the "n"th space in the sphere spectrum is the "n"-dimensional sphere "S", and the structure maps from the suspension of "S" to "S" are the canonical homeomorphisms. The "k"-th homotopy group of a sphere spectrum is the "k"-th stable homotopy group of spheres. The localization of the sphere spectrum at a prime number "p" is called the local sphere at "p" and is