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Given four points chosen at random inside a unit cube, the average volume of the tetrahedron determined by these points is given by ...

The mean triangle area of a triangle picked at random inside a unit cube is A^_=0.15107+/-0.00003, with variance var(A)=0.008426+/-0.000004. The distribution of areas, ...

A graph G is said to be disconnected if it is not connected, i.e., if there exist two nodes in G such that no path in G has those nodes as endpoints. The numbers of ...

An edge cover is a subset of edges defined similarly to the vertex cover (Skiena 1990, p. 219), namely a collection of graph edges such that the union of edge endpoints ...

The functions E_1(x) = (x^2e^x)/((e^x-1)^2) (1) E_2(x) = x/(e^x-1) (2) E_3(x) = ln(1-e^(-x)) (3) E_4(x) = x/(e^x-1)-ln(1-e^(-x)). (4) E_1(x) has an inflection point at (5) ...

The elliptic exponential function eexp_(a,b)(u) gives the value of x in the elliptic logarithm eln_(a,b)(x)=1/2int_infty^x(dt)/(sqrt(t^3+at^2+bt)) for a and b real such that ...

The elliptic logarithm is generalization of integrals of the form int_infty^x(dt)/(sqrt(t^2+at)), for a real, which can be expressed in terms of logarithmic and inverse ...

Engineering notation is a version of scientific notation in which the exponent p in expressions of the form a×10^p is chosen to always be divisible by 3. Numbers of forms ...

Euler's continued fraction is the name given by Borwein et al. (2004, p. 30) to Euler's formula for the inverse tangent, ...

A fallacy is an incorrect result arrived at by apparently correct, though actually specious reasoning. The great Greek geometer Euclid wrote an entire book on geometric ...