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A harmonic number is a number of the form H_n=sum_(k=1)^n1/k (1) arising from truncation of the harmonic series. A harmonic number can be expressed analytically as ...

The Heawood graph is a cubic graph on 14 vertices and 21 edges which is the unique (3,6)-cage graph. It is also a Moore graph. It has graph diameter 3, graph radius 3, and ...

Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

"The" octahedral graph is the 6-node 12-edge Platonic graph having the connectivity of the octahedron. It is isomorphic to the circulant graph Ci_6(1,2), the cocktail party ...

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 ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

An arithmetic progression of primes is a set of primes of the form p_1+kd for fixed p_1 and d and consecutive k, i.e., {p_1,p_1+d,p_1+2d,...}. For example, 199, 409, 619, ...