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Consider the distribution of distances l between a point picked at random in the interior of a unit cube and on a face of the cube. The probability function, illustrated ...

Let P=alpha:beta:gamma be a point not on a sideline of a reference triangle DeltaABC. Let A^' be the point of intersection AP intersection BC, B^'=BP intersection AC, and ...

Numbers which are not perfect and for which s(N)=sigma(N)-N<N, or equivalently sigma(n)<2n, where sigma(N) is the divisor function. Deficient numbers are sometimes called ...

A theorem proved by Doob (1942) which states that any random process which is both normal and Markov has the following forms for its correlation function C_y(tau), spectral ...

Consider a point P inside a reference triangle DeltaABC, construct line segments AP, BP, and CP. The Ehrmann congruent squares point is the unique point P such that three ...

There exists a triangulation point Y for which the triangles BYC, CYA, and AYB have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and ...

The Erdős-Borwein constant E, sometimes also denoted alpha, is the sum of the reciprocals of the Mersenne numbers, E = sum_(n=1)^(infty)1/(2^n-1) (1) = ...

The Evans conic is the conic section passing through the Fermat points X and X^', the inner and outer Napoleon points N and N^', and the isodynamic points S and S^' of a ...

The even part Ev(n) of a positive integer n is defined by Ev(n)=2^(b(n)), where b(n) is the exponent of the exact power of 2 dividing n. The values for n=1, 2, ..., are 1, 2, ...

The Feller-Tornier constant is the density of integers that have an even number of prime factors p_i^(a_i) with a_1>1 in their prime factorization. It is given by ...