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A self-avoiding walk is a path from one point to another which never intersects itself. Such paths are usually considered to occur on lattices, so that steps are only allowed ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

A Mersenne prime is a Mersenne number, i.e., a number of the form M_n=2^n-1, that is prime. In order for M_n to be prime, n must itself be prime. This is true since for ...

The ordinal number of a value in a list arranged in a specified order (usually decreasing).

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

A number is said to be pandigital if it contains each of the digits from 0 to 9 (and whose leading digit must be nonzero). However, "zeroless" pandigital quantities contain ...

There are a few plane curves known as "bean curves." The bean curve identified by Cundy and Rowllet (1989, p. 72) is the quartic curve given by the implicit equation ...

A curve also known as the Gerono lemniscate. It is given by Cartesian coordinates x^4=a^2(x^2-y^2), (1) polar coordinates, r^2=a^2sec^4thetacos(2theta), (2) and parametric ...

The largest value of a set, function, etc. The maximum value of a set of elements A={a_i}_(i=1)^N is denoted maxA or max_(i)a_i, and is equal to the last element of a sorted ...

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