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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 ...

If the coefficients of the polynomial d_nx^n+d_(n-1)x^(n-1)+...+d_0=0 (1) are specified to be integers, then rational roots must have a numerator which is a factor of d_0 and ...

Pick two real numbers x and y at random in (0,1) with a uniform distribution. What is the probability P_(even) that [x/y], where [r] denotes the nearest integer function, is ...

The number of ways N(m,n) of finding a subrectangle with an m×n rectangle can be computed by counting the number of ways in which the upper right-hand corner can be selected ...

A strict order > on the set of terms of a term rewriting system is called a reduction order if 1. The set of terms is well ordered with respect to >, that is, all its ...

A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma ...

The regular hendecagon is the regular polygon with 11 sides, as illustrated above, and has Schläfli symbol {11}. The regular hendecagon cannot be constructed using the ...

The regularized gamma functions are defined by P(a,z) = (gamma(a,z))/(Gamma(a)) (1) Q(a,z) = (Gamma(a,z))/(Gamma(a)), (2) where gamma(a,z) and Gamma(a,z) are incomplete gamma ...

In the 1930s, Reidemeister first rigorously proved that knots exist which are distinct from the unknot. He did this by showing that all knot deformations can be reduced to a ...

Relaxation methods are methods of solving partial differential equations that involve splitting the sparse matrix that arises from finite differencing then iterating until a ...