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The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area ...

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

If a sequence has the property that the block growth function B(n)=n+1 for all n, then it is said to have minimal block growth, and the sequence is called a Sturmian ...

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...

Let E be a linear space over a field K. Then the vector space tensor product tensor _(lambda=1)^(k)E is called a tensor space of degree k. More specifically, a tensor space ...

Let p be an irregular prime, and let P=rp+1 be a prime with P<p^2-p. Also let t be an integer such that t^3≢1 (mod P). For an irregular pair (p,2k), form the product ...

If at least one of d, e, or f has the form q^(-N) for some nonnegative integer N (in which case both sums terminate after N+1 terms), then ...

The Werner formulas are the trigonometric product formulas 2sinalphacosbeta = sin(alpha-beta)+sin(alpha+beta) (1) 2cosalphacosbeta = cos(alpha-beta)+cos(alpha+beta) (2) ...

Suppose W is the set of all complex-valued functions f on the interval [0,2pi] of the form f(t)=sum_(k=-infty)^inftyalpha_ke^(ikt) (1) for t in [0,2pi], where the alpha_k in ...

In the Wolfram Language, WignerD[{j, m ,n}, psi, theta, phi] gives the m×n matrix element of a (2j+1)-dimensional unitary representation of SU(2) parametrized by three Euler ...