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A sliver of the surface of a sphere of radius r cut out by two planes through the azimuthal axis with dihedral angle theta. The surface area of the lune is S=2r^2theta, which ...

In the process of attaching a k-handle to a manifold M, the boundary of M is modified by a process called (k-1)-surgery. Surgery consists of the removal of a tubular ...

The Riemann sphere C^*=C union {infty}, also called the extended complex plane. The notation C^^ is sometimes also used (Krantz 1999, p. 82). The notation C^* is also used to ...

The circle with respect to which an inverse curve is computed or relative to which inverse points are computed. In three dimensions, inverse points can be computed relative ...

The complex plane C with the origin removed, i.e., C-{0}. The punctured plane is sometimes denoted C^* (although this notation conflicts with that for the Riemann sphere C-*, ...

Consider two mutually tangent (externally) spheres A and B together with a larger sphere C inside which A and B are internally tangent. Then construct a chain of spheres each ...

A map projection obtained by projecting points P on the surface of sphere from the sphere's north pole N to point P^' in a plane tangent to the south pole S (Coxeter 1969, p. ...

A simple closed curve on a sphere that is not necessarily a great circle but merely intersects as a great circle would (Billera et al. 1999).

Any nontrivial, closed, simple, smooth spherical curve dividing the surface of a sphere into two parts of equal areas has at least four inflection points.

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...