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The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...

An Archimedean spiral with polar equation r=a/theta. (1) The hyperbolic spiral, also called the inverse spiral (Whittaker 1944, p. 83), originated with Pierre Varignon in ...

The Jordan matrix decomposition is the decomposition of a square matrix M into the form M=SJS^(-1), (1) where M and J are similar matrices, J is a matrix of Jordan canonical ...

Lissajous curves are the family of curves described by the parametric equations x(t) = Acos(omega_xt-delta_x) (1) y(t) = Bcos(omega_yt-delta_y), (2) sometimes also written in ...

A formula which transforms a given coordinate system by rotating it through a counterclockwise angle Phi about an axis n^^. Referring to the above figure (Goldstein 1980), ...

Let C be a curve, let O be a fixed point (the pole), and let O^' be a second fixed point. Let P and P^' be points on a line through O meeting C at Q such that P^'Q=QP=QO^'. ...

Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

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 ...

The genesa is a mystical figure that correspond to a spherical cuboctahedron.

A shell bounded by two similar ellipsoids having a constant ratio of axes. Given a chord passing through a homeoid, the distance between inner and outer intersections is ...