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There are several meanings of the word content in mathematics. The content of a polytope or other n-dimensional object is its generalized volume (i.e., its "hypervolume"). ...

In two-dimensional polar coordinates, the Helmholtz differential equation is 1/rpartial/(partialr)(r(partialF)/(partialr))+1/(r^2)(partial^2F)/(partialtheta^2)+k^2F=0. (1) ...

A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

The technique of extracting the content from geometric (tensor) equations by working in component notation and rearranging indices as required. Index gymnastics is a ...

In the above figure, let DeltaABC be a right triangle, arcs AP and AQ be segments of circles centered at C and B respectively, and define a = BC (1) b = CA=CP (2) c = BA=BQ. ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

The spherical harmonics Y_l^m(theta,phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. Some ...

The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...

A generalization of Schröter's formula.