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The fast Fourier transform (FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for N points from 2N^2 to 2NlgN, where lg is the ...

There are at least three definitions of "groupoid" currently in use. The first type of groupoid is an algebraic structure on a set with a binary operator. The only ...

A Hamilton decomposition (also called a Hamiltonian decomposition; Bosák 1990, p. 123) of a Hamiltonian regular graph is a partition of its edge set into Hamiltonian cycles. ...

There are a number of algebraic equations known as the icosahedral equation, all of which derive from the projective geometry of the icosahedron. Consider an icosahedron ...

The Jacobi triple product is the beautiful identity product_(n=1)^infty(1-x^(2n))(1+x^(2n-1)z^2)(1+(x^(2n-1))/(z^2))=sum_(m=-infty)^inftyx^(m^2)z^(2m). (1) In terms of the ...

A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in R^n). ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

The permutation symbol (Evett 1966; Goldstein 1980, p. 172; Aris 1989, p. 16) is a three-index object sometimes called the Levi-Civita symbol (Weinberg 1972, p. 38; Misner et ...

secz is the trigonometric function defined by secz = 1/(cosz) (1) = 2/(e^(iz)+e^(-iz)), (2) where cosz is the cosine. The secant is implemented in the Wolfram Language as ...

A number which is simultaneously square and triangular. Let T_n denote the nth triangular number and S_m the mth square number, then a number which is both triangular and ...