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Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

A portion of a disk whose upper boundary is a (circular) arc and whose lower boundary is a chord making a central angle theta<pi radians (180 degrees), illustrated above as ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

Let A be an n×n real square matrix with n>=2 such that |sum_(i=1)^nsum_(j=1)^na_(ij)s_it_j|<=1 (1) for all real numbers s_1, s_2, ..., s_n and t_1, t_2, ..., t_n such that ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

Complex Analysis

The 24-cell is a finite regular four-dimensional polytope with Schläfli symbol {3,4,3}. It is also known as the hyperdiamond or icositetrachoron, and is composed of 24 ...

Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...

The banner graph is the (4,1)-tadpole graph illustrated above. It could perhaps also be termed the 'P graph.' It is implemented in the Wolfram Language as ...

The bipartite double graph, also called the Kronecker cover, Kronecker double cover, bipartite double cover, canonical double cover, or bipartite double, of a given graph G ...