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There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

Chebyshev iteration is a method for solving nonsymmetric problems (Golub and van Loan 1996, §10.1.5; Varga, 1962, Ch. 5). Chebyshev iteration avoids the computation of inner ...

A n-crossed prism graph for positive even n (a term introduced here for the first time), is a graph obtained by taking two disjoint cycle graphs C_n and adding edges ...

An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is ...

The most general form of "an" exponential function is a power-law function of the form f(x)=ab^(cx+d), (1) where a, c, and d are real numbers, b is a positive real number, ...

The Hall-Janko graph, also known as the Hall-Janko-Wales graph, is a strongly regular graph on 100 nodes with parameters (nu,k,lambda,mu)=(100,36,14,12). It is also a ...

An equation involving a function f(x) and integrals of that function to solved for f(x). If the limits of the integral are fixed, an integral equation is called a Fredholm ...

The Jacobi triple product is the beautiful identity product_(n=1)^infty(1-x^(2n))(1+x^(2n-1)z^2)(1+(x^(2n-1))/(z^2))=sum_(m=-infty)^inftyx^(m^2)z^(2m). (1) In terms of the ...

The Klein graph is a weakly regular graph that is the dual graph of the cubic symmetric graph F_(056)B. The Klein graph is illustrated above in four order-4 LCF notations. ...