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Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane ax+by+cz+d=0 (1) by defining the ...

A two-component complex column vector. Spinors can describe both bosons and fermions, while tensors can describe only bosons.

Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

The triangular orthobicupola is Johnson solid J_(27), consisting of eight equilateral triangles and six squares. If a triangular orthobicupola is oriented with triangles on ...

An affine tensor is a tensor that corresponds to certain allowable linear coordinate transformations, T:x^_^i=a^i_jx^j, where the determinant of a^i_j is nonzero. This ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

The term "bundle" is an abbreviated form of the full term fiber bundle. Depending on context, it may mean one of the special cases of fiber bundles, such as a vector bundle ...

The functions describing the horizontal and vertical positions of a point on a circle as a function of angle (cosine and sine) and those functions derived from them: cotx = ...