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Power formulas include sin^2x = 1/2[1-cos(2x)] (1) sin^3x = 1/4[3sinx-sin(3x)] (2) sin^4x = 1/8[3-4cos(2x)+cos(4x)] (3) and cos^2x = 1/2[1+cos(2x)] (4) cos^3x = ...

A module having only one element: the singleton set {*}. It is a module over any ring R with respect to the multiplication defined by a*=* (1) for every a in R, and the ...

The truncated dodecadodecahedron, also called the quasitruncated dodecahedron, is the uniform polyhedron with Maeder index 59 (Maeder 1997), Wenninger index 98 (Wenninger ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* may or may not separate points (i.e., may or may not be T2). The weak-* (pronounced "weak star") ...

An analytic function approaches any given value arbitrarily closely in any epsilon-neighborhood of an essential singularity.

Wolfram's iteration is an algorithm for computing the square root of a rational number 1<=r<4 using properties of the binary representation of r. The algorithm begins with ...

A zero matrix is an m×n matrix consisting of all 0s (MacDuffee 1943, p. 27), denoted 0. Zero matrices are sometimes also known as null matrices (Akivis and Goldberg 1972, p. ...

About Eric Weisstein's World of Mathematics

The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

An alternating group is a group of even permutations on a set of length n, denoted A_n or Alt(n) (Scott 1987, p. 267). Alternating groups are therefore permutation groups. ...