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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 ...

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 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.

Long division is an algorithm for dividing two numbers, obtaining the quotient one digit at a time. The example above shows how the division of 123456/17 is performed to ...

Machin's formula is given by 1/4pi=4cot^(-1)5-cot^(-1)239. There are a whole class of Machin-like formulas with various numbers of terms (although only four such formulas ...

If one looks inside a flat origami without unfolding it, one sees a zigzagged profile, determined by an alternation of "mountain-creases" and "valley-creases." The numbers of ...

Let x=(x_1,x_2,...,x_n) and y=(y_1,y_2,...,y_n) be nonincreasing sequences of real numbers. Then x majorizes y if, for each k=1, 2, ..., n, sum_(i=1)^kx_i>=sum_(i=1)^ky_i, ...