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The Champernowne constant has decimal expansion C=0.1234567891011... (OEIS A033307). The Earls sequence (starting position of n copies of the digit n) for e is given for n=1, ...

Define the abundancy Sigma(n) of a positive integer n as Sigma(n)=(sigma(n))/n, (1) where sigma(n) is the divisor function. Then a pair of distinct numbers (k,m) is a ...

The gnomon was an L-shaped movable sundial used for astronomical studies. It operated by resting on one leg so that the other pointed vertically upward. By measuring the ...

In 1913, Ramanujan asked if the Diophantine equation of second order 2^n-7=x^2, sometimes called the Ramanujan-Nagell equation, has any solutions other than n=3, 4, 5, 7, and ...

Ruffini's rule a shortcut method for dividing a polynomial by a linear factor of the form x-a which can be used in place of the standard long division algorithm. This method ...

Given a function f(x)=f_0(x), write f_1=f^'(x) and define the Sturm functions by f_n(x)=-{f_(n-2)(x)-f_(n-1)(x)[(f_(n-2)(x))/(f_(n-1)(x))]}, (1) where [P(x)/Q(x)] is a ...

Chess is a two-player board game believed to have been played in India as early as the sixth century AD. In different parts of this world, different chess games are played. ...

A property of motion which is conserved to exponential accuracy in the small parameter representing the typical rate of change of the gross properties of the body.

A category of link encompassing both alternating knots and torus knots.

A solution to a problem that can be written in "closed form" in terms of known functions, constants, etc., is often called an analytic solution. Note that this use of the ...