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Two families of equations used to find roots of nonlinear functions of a single variable. The "B" family is more robust and can be used in the neighborhood of degenerate ...

A conformal mapping from the upper half-plane to a polygon.

Let f be analytic on the unit disk, and assume that 1. |f(z)|<=1 for all z, and 2. f(a)=b for some a,b in D(0,1), the unit disk. Then |f^'(a)|<=(1-|b|^2)/(1-|a|^2). (1) ...

The Schwarz triangles are spherical triangles which, by repeated reflection in their indices, lead to a set of congruent spherical triangles covering the sphere a finite ...

A periodic minimal surface constructed by Schwarz using the following two principles: 1. If part of the boundary of a minimal surface is a straight line, then the reflection ...

A polyhedron constructed by ruling 2n equally spaced vertical lines along the surface of a cylinder together with 2n^3 circles around the cylinder at equally spaced heights. ...

Scientific notation is the expression of a number n in the form a×10^p, where p=|_log_(10)|n|_| (1) is the floor of the base-10 logarithm of n (the "order of magnitude"), and ...

Sea horse valley is a name sometimes given to the portion of the Mandelbrot set centered around -0.75+0.1i.

A conical surface modeled after the shape of a seashell. One parameterization (left figure) is given by x = 2[1-e^(u/(6pi))]cosucos^2(1/2v) (1) y = ...

A root-finding algorithm which assumes a function to be approximately linear in the region of interest. Each improvement is taken as the point where the approximating line ...