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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 ...

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

The logarithm log_bx for a base b and a number x is defined to be the inverse function of taking b to the power x, i.e., b^x. Therefore, for any x and b, x=log_b(b^x), (1) or ...

A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function ...

Convergents of the pi continued fractions are the simplest approximants to pi. The first few are given by 3, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, ... (OEIS ...

A finite set of contraction maps w_i for i=1, 2, ..., N, each with a contractivity factor s<1, which map a compact metric space onto itself. It is the basis for fractal image ...

An object is amphichiral (also called reflexible) if it is superposable with its mirror image (i.e., its image in a plane mirror).

The span of an unoriented link diagram (also called the link spread) is the difference between the highest and lowest degrees of its bracket polynomial. The span is a ...

The dimension of a partially ordered set P=(X,<=) is the size of the smallest realizer of P. Equivalently, it is the smallest integer d such that P is isomorphic to a ...

The rectifiable sets include the image of any Lipschitz function f from planar domains into R^3. The full set is obtained by allowing arbitrary measurable subsets of ...