Stereographic: Any circle of a sphere, great and small, maps to a circle or straight line.

A circle of a sphere can also be defined as the set of points at a given angular distance from a given pole.

A circle of a sphere is a circle defined as the intersection of a sphere and a plane.

In the spherical representation of elliptic geometry, lines are represented by great circles of a sphere with diametrically opposite points identified.

Circles of a sphere have radius less than or equal to the sphere radius, with equality when the circle is a great circle.

Thus, in spherical geometry, where lines are represented in the standard model by great circles of a sphere, sets of collinear points lie on the same great circle.

The Imperial and U.S. definitions of the nautical mile were based on the Clarke (1866) Spheroid: they were different approximations to the length of one minute of arc along a great circle of a sphere having the same surface area as the Clarke Spheroid.

A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center.