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The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric ...

A procedure for finding the quadratic factors for the complex conjugate roots of a polynomial P(x) with real coefficients. (1) Now write the original polynomial as ...

If a function phi:(0,infty)->(0,infty) satisfies 1. ln[phi(x)] is convex, 2. phi(x+1)=xphi(x) for all x>0, and 3. phi(1)=1, then phi(x) is the gamma function Gamma(x). ...

A set of planes sharing a point in common. For planes specified in Hessian normal form, a bundle of planes can therefore be specified as ...

Given a positive sequence {a_n}, sqrt(sum_(j=-infty)^infty|sum_(n=-infty; n!=j)^infty(a_n)/(j-n)|^2)<=pisqrt(sum_(n=-infty)^infty|a_n|^2), (1) where the a_ns are real and ...

A type of plot invented by M. Trott that shows the behavior of a function near and far from the origin simultaneously. Inside a given radius, the plot shows the actual value ...

A topological space is locally connected at the point x if every neighborhood of x contains a connected open neighborhood. It is called locally connected if it is locally ...

A logarithmic singularity is a singularity of an analytic function whose main z-dependent term is of order O(lnz). An example is the singularity of the Bessel function of the ...

Let A=a_(ij) be an n×n matrix with complex (or real) entries and eigenvalues lambda_1, lambda_2, ..., lambda_n, then sum_(i=1)^n|lambda_i|^2<=sum_(i,j=1)^n|a_(ij)|^2 (1) ...

A plot of a function expressed in spherical coordinates, with radius r as a function of angles theta and phi. Polar plots can be drawn using SphericalPlot3D[r, {phi, phimin, ...