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For every ring containing p spheres, there exists a ring of q spheres, each touching each of the p spheres, where 1/p+1/q=1/2, (1) which can also be written (p-2)(q-2)=4. (2) ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

Let F be the set of complex analytic functions f defined on an open region containing the closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each f in ...

A Laurent polynomial with coefficients in the field F is an algebraic object that is typically expressed in the form ...+a_(-n)t^(-n)+a_(-(n-1))t^(-(n-1))+... ...

To fit a functional form y=Ae^(Bx), (1) take the logarithm of both sides lny=lnA+Bx. (2) The best-fit values are then a = ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

Let mu(sigma) be the least upper bound of the numbers A such that |zeta(sigma+it)|t^(-A) is bounded as t->infty, where zeta(s) is the Riemann zeta function. Then the Lindelöf ...

The symbol o(x), pronounced "little-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n ...

The unique magic square of order three. The Lo Shu is an associative magic square, but not a panmagic square.

There are no fewer than three distinct notions of the term local C^*-algebra used throughout functional analysis. A normed algebra A=(A,|·|_A) is said to be a local ...