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The distance from the center of a circle to its perimeter, or from the center of a sphere to its surface. The radius is equal to half the diameter.

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...

A group of three elements, also called a triad. A triple is therefore a 3-tuple.

A zero tensor is a tensor of any rank and with any pattern of covariant and contravariant indices all of whose components are equal to 0 (Weinberg 1972, p. 38).

Written in the notation of partial derivatives, the d'Alembertian square ^2 in a flat spacetime is defined by square ^2=del ^2-1/(c^2)(partial^2)/(partialt^2), where c is the ...

If r is a root of a nonzero polynomial equation a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the a_is are integers (or equivalently, rational numbers) and r satisfies no ...

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

A category consists of three things: a collection of objects, for each pair of objects a collection of morphisms (sometimes call "arrows") from one to another, and a binary ...