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The inequality sinAsinBsinC<=((3sqrt(3))/(2pi))^3ABC, where A, B, and C are the vertex angles of a triangle. The maximum is reached for an equilateral triangle (and therefore ...

An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct ...

Algebraic number theory is the branch of number theory that deals with algebraic numbers. Historically, algebraic number theory developed as a set of tools for solving ...

Algorithmic graph theory is the study of graph traversal and generation and the complexity of these operations. Topics in algorithmic graph theory include Eulerian and ...

An amicable quadruple as a quadruple (a,b,c,d) such that sigma(a)=sigma(b)=sigma(c)=sigma(d)=a+b+c+d, (1) where sigma(n) is the divisor function. If (a,b) and (x,y) are ...

Dickson (1913, 2005) defined an amicable triple to be a triple of three numbers (l,m,n) such that s(l) = m+n (1) s(m) = l+n (2) s(n) = l+m, (3) where s(n) is the restricted ...

R. C. Read defined the anarboricity of a graph G as the maximum number of edge-disjoint nonacyclic (i.e., cyclic) subgraphs of G whose union is G (Harary and Palmer 1973, p. ...

A plane tiling is said to be isohedral if the symmetry group of the tiling acts transitively on the tiles, and n-isohedral if the tiles fall into n orbits under the action of ...

Given a graph G, the arboricity Upsilon(G) is the minimum number of edge-disjoint acyclic subgraphs (i.e., spanning forests) whose union is G. An acyclic graph therefore has ...

Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_(2n) and b_(2n) the perimeters of the circumscribed and inscribed 2n-gon. Then a_(2n) = ...