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A regular continued fraction is a simple continued fraction x = b_0+1/(b_1+1/(b_2+1/(b_3+...))) (1) = K_(k=1)^(infty)1/(b_k) (2) = [b_0;b_1,b_2,...], (3) where b_0 is an ...

"Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form z^3+a_2z^2+a_1z+a_0=0 (1) ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

Generally speaking, a Green's function is an integral kernel that can be used to solve differential equations from a large number of families including simpler examples such ...

There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

The Spencer-Brown form is a simple mathematical concept that formalizes what a mathematical object is formally identical to what it is not (Spencer-Brown 1997, pp. ix and ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...