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Let p be an odd prime, a be a positive number such that pa (i.e., p does not divide a), and let x be one of the numbers 1, 2, 3, ..., p-1. Then there is a unique x^', called ...

Given a function f(x) plotted in the Cartesian plane as y=f(x), the average rate of change (or average rate of change function) of f from x to a is given by ...

The binomial distribution gives the discrete probability distribution P_p(n|N) of obtaining exactly n successes out of N Bernoulli trials (where the result of each Bernoulli ...

An operator Gamma=sum_(i=1)^me_i^Ru^(iR) on a representation R of a Lie algebra.

The parametric equations for a catenary are x = t (1) y = acosh(t/a), (2) giving the evolute as x = t-a/2sinh((2t)/a) (3) y = 2acosh(t/(2a)). (4) For t>0, the evolute has arc ...

An n-dimensional closed disk of radius r is the collection of points of distance <=r from a fixed point in n-dimensional Euclidean space. Krantz (1999, p. 3) uses the symbol ...

A set X is called a "cone" with vertex at the origin if for any x in X and any scalar a>=0, ax in X.

The difference of a quantity from some fixed value, usually the "correct" or "expected" one.

A diagonal of a square matrix which is traversed in the "southeast" direction. "The" diagonal (or "main diagonal," or "principal diagonal," or "leading diagonal") of an n×n ...

A quantity defined for a conic section which can be given in terms of semimajor a and semiminor axes b. interval curve e e=0 circle 0 0<e<1 ellipse sqrt(1-(b^2)/(a^2)) e=1 ...