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The series sum_(j=1)^(infty)f_j(z) is said to be uniformly Cauchy on compact sets if, for each compact K subset= U and each epsilon>0, there exists an N>0 such that for all ...

If f is a continuous real-valued function on [a,b] and if any epsilon>0 is given, then there exists a polynomial p on [a,b] such that |f(x)-P(x)|<epsilon for all x in [a,b]. ...

The Zeckendorf representation of a positive integer n is a representation of n as a sum of nonconsecutive distinct Fibonacci numbers, n=sum_(k=2)^Lepsilon_kF_k, where ...

There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a ...

When a point P moves along a line through the circumcenter of a given triangle Delta, the pedal circle of P with respect to Delta passes through a fixed point (the Griffiths ...

A two-graph (V,Delta) on nodes V is a collection Delta of unordered triples of the vertices (the so-called "odd triples") such that each 4-tuple of V contains an even number ...

The central difference for a function tabulated at equal intervals f_n is defined by delta(f_n)=delta_n=delta_n^1=f_(n+1/2)-f_(n-1/2). (1) First and higher order central ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

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 ...

The Laplacian for a scalar function phi is a scalar differential operator defined by (1) where the h_i are the scale factors of the coordinate system (Weinberg 1972, p. 109; ...