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Let x=(x_1,x_2,...,x_n) and y=(y_1,y_2,...,y_n) be nonincreasing sequences of real numbers. Then x majorizes y if, for each k=1, 2, ..., n, sum_(i=1)^kx_i>=sum_(i=1)^ky_i, ...

The three circumcircles through the triangle centroid G of a given triangle DeltaA_1A_2A_3 and the pairs of the vertices of the second Brocard triangle are called the McCay ...

A plot of the cells on a grid satisfying bitwise XOR(a,b)<n for consecutive values of n=1, 2, .... It is thought that it was discovered by Jackson Wright on the RLE PDP-1 ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

Given a parabola with parametric equations x = at^2 (1) y = 2at, (2) the negative pedal curve for a pedal point (x_0,0) has equation x_n = (at^2[a(3t^2+4)-x_0])/(at^2+x_0) ...

Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." For example, ...

According to G. Pólya, the method of finding geometric objects by intersection. 1. For example, the centers of all circles tangent to a straight line s at a given point P lie ...

The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints. This theorem can be applied to determine the center of a ...

The path traced out by a fixed point at a radius b>a, where a is the radius of a rolling circle, also sometimes called an extended cycloid. The prolate cycloid contains ...

Let a closed interval [a,b] be partitioned by points a<x_1<x_2<...<x_(n-1)<b, where the lengths of the resulting intervals between the points are denoted Deltax_1, Deltax_2, ...