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In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Dickson 2005, p. 3), although this method applies only to even perfect numbers. In a 1638 ...

Let Sigma(n)=sum_(i=1)^np_i (1) be the sum of the first n primes (i.e., the sum analog of the primorial function). The first few terms are 2, 5, 10, 17, 28, 41, 58, 77, ... ...

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 classic treatise in geometry written by Euclid and used as a textbook for more than 1000 years in western Europe. An Arabic version The Elements appears at the end of the ...

A great circle is a section of a sphere that contains a diameter of the sphere (Kern and Bland 1948, p. 87). Sections of the sphere that do not contain a diameter are called ...

A Heronian tetrahedron, also called a perfect tetrahedron, is a (not necessarily regular) tetrahedron whose sides, face areas, and volume are all rational numbers. It ...

The incidence matrix of a graph gives the (0,1)-matrix which has a row for each vertex and column for each edge, and (v,e)=1 iff vertex v is incident upon edge e (Skiena ...

The radius of a polygon's incircle or of a polyhedron's insphere, denoted r or sometimes rho (Johnson 1929). A polygon possessing an incircle is same to be inscriptable or ...

Given a function f(x) of a variable x tabulated at m values y_1=f(x_1), ..., y_m=f(x_m), assume the function is of known analytic form depending on n parameters ...

The concept of "random close packing" was shown by Torquato et al. (2000) to be mathematically ill-defined idea that is better replaced by the notion of "maximally random ...