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A tag system is set of rules that specifies a fixed number of elements (commonly denoted nu or beta) be removed from the beginning of a sequence and a set of elements to be ...

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...

In a given triangle DeltaABC with all angles less than 120 degrees (2pi/3, the first Fermat point X or F_1 (sometimes simply called "the Fermat point," Torricelli point, or ...

The straight line on which all points at infinity lie. The line at infinity is central line L_6 (Kimberling 1998, p. 150), and has trilinear equation aalpha+bbeta+cgamma=0, ...

The logarithmic spiral is a spiral whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and ...

Given a triangle DeltaABC, the triangle DeltaH_AH_BH_C whose vertices are endpoints of the altitudes from each of the vertices of DeltaABC is called the orthic triangle, or ...

The general bivariate quadratic curve can be written ax^2+2bxy+cy^2+2dx+2fy+g=0. (1) Define the following quantities: Delta = |a b d; b c f; d f g| (2) J = |a b; b c| (3) I = ...