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Consider an n-dimensional deterministic dynamical system x^_^.=f^_(x) and let S be an n-1-dimensional surface of section that is traverse to the flow, i.e., all trajectories ...

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...

The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric ...

A polyhedron is said to be canonical if all its polyhedron edges touch a sphere and the center of gravity of their contact points is the center of that sphere. In other ...

If a, b, c, and d are points in the extended complex plane C^*, their cross ratio, also called the cross-ratio (Courant and Robbins 1996, p. 172; Durell 1928, p. 73), ...

The polar angle on a sphere measured from the north pole instead of the equator. The angle phi in spherical coordinates is the colatitude. It is related to the latitude delta ...

A map projection in which the distances between one or two points and every other point on the map differ from the corresponding distances on the sphere by only a constant ...

When applied to a system possessing a length R at which solutions in a variable r change character (such as the gravitational field of a sphere as r runs from the interior to ...

A hosohedron is a regular tiling or map on a sphere composed of p digons or spherical lunes, all with the same two vertices and the same vertex angles, 2pi/p. Its Schläfli ...

If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...