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The representation, beloved of engineers and physicists, of a complex number in terms of a complex exponential x+iy=|z|e^(iphi), (1) where i (called j by engineers) is the ...

A pivotal isotomic cubic is a self-isotomic cubic that possesses a pivot point, i.e., in which points P lying on the conic and their isotomic conjugates are collinear with a ...

A map defined by one or more polynomials. Given a field K, a polynomial map is a map f:K^n->K^m such that for all points (x_1,...,x_n) in K^n, ...

Let the two-dimensional cylinder function be defined by f(x,y)={1 for r<R; 0 for r>R. (1) Then the Radon transform is given by ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

A regular pyramid is a right pyramid whose base is a regular polygon. For a right pyramid of height h with a regular n-gonal base of side length a and circumradius R, the ...

There exist infinitely many odd integers k such that k·2^n-1 is composite for every n>=1. Numbers k with this property are called Riesel numbers, while analogous numbers with ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...

Rule 182 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

When computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is ...