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The conjecture that all integers >1 occur as a value of the totient valence function (i.e., all integers >1 occur as multiplicities). The conjecture was proved by Ford ...

There appear to be two different definitions of the standard error. The standard error of a sample of sample size n is the sample's standard deviation divided by sqrt(n). It ...

The term "range" has two completely different meanings in statistics. Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j, the range of the random sample ...

The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 2000, p. 6). The survival function is therefore ...

The weighted mean of a discrete set of numbers {x_1,x_2,...,x_n} with weights {w_1,w_2,...,w_n} is given by <x>=sum_(i=1)^nw_ix_i, (1) where each weight w_i is a nonnegative ...

Let a_(n+1) = 1/2(a_n+b_n) (1) b_(n+1) = (2a_nb_n)/(a_n+b_n). (2) Then A(a_0,b_0)=lim_(n->infty)a_n=lim_(n->infty)b_n=sqrt(a_0b_0), (3) which is just the geometric mean.

An "area" which can be defined for every set--even those without a true geometric area--which is rigid and finitely additive.

Cube duplication, also called the Delian problem, is one of the geometric problems of antiquity which asks, given the length of an edge of a cube, that a second cube be ...

The reciprocal of the arithmetic-geometric mean of 1 and sqrt(2), G = 2/piint_0^11/(sqrt(1-x^4))dx (1) = 2/piint_0^(pi/2)(dtheta)/(sqrt(1+sin^2theta)) (2) = L/pi (3) = ...

A geometric figure which touches only the sides (or interior) of another figure.