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The real projective plane is the closed topological manifold, denoted RP^2, that is obtained by projecting the points of a plane E from a fixed point P (not on the plane), ...

The rotation operator can be derived from examining an infinitesimal rotation (d/(dt))_(space)=(d/(dt))_(body)+omegax, where d/dt is the time derivative, omega is the angular ...

A Kähler structure on a complex manifold M combines a Riemannian metric on the underlying real manifold with the complex structure. Such a structure brings together geometry ...

A Lorentz transformation is a four-dimensional transformation x^('mu)=Lambda^mu_nux^nu, (1) satisfied by all four-vectors x^nu, where Lambda^mu_nu is a so-called Lorentz ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

Hex is a two-player game invented by Piet Hein in 1942 while a student at Niels Bohr's Institute for Theoretical Physics, and subsequently and independently by John Nash in ...

A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...

A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and ...

Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Pawley (1973) gave a set of restrictions ...