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Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

With three cuts, dissect an equilateral triangle into a square. The problem was first proposed by Dudeney in 1902, and subsequently discussed in Dudeney (1958), and Gardner ...

Let f be an entire function of finite order lambda and {a_j} the zeros of f, listed with multiplicity, then the rank p of f is defined as the least positive integer such that ...

The Hadamard product is a representation for the Riemann zeta function zeta(s) as a product over its nontrivial zeros rho, ...

A linear functional defined on a subspace of a vector space V and which is dominated by a sublinear function defined on V has a linear extension which is also dominated by ...

The orthogonal polynomials defined by h_n^((alpha,beta))(x,N)=((-1)^n(N-x-n)_n(beta+x+1)_n)/(n!) ×_3F_2(-n,-x,alpha+N-x; N-x-n,-beta-x-n;1) =((-1)^n(N-n)_n(beta+1)_n)/(n!) ...

A Hajós group is a group for which all factorizations of the form (say) Z_n=A direct sum B have A or B periodic, where the period is a divisor of n. Hajós groups arose after ...

The half-altitude triangle DeltaA^'B^'C^' of a reference triangle DeltaABC is defined by letting A^' be the midpoint between vertex A and the foot of the A-altitude on side ...

Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...

In the study of non-associative algebra, there are at least two different notions of what the half-Bol identity is. Throughout, let L be an algebraic loop and let x, y, and z ...