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A circular sector is a wedge obtained by taking a portion of a disk with central angle theta<pi radians (180 degrees), illustrated above as the shaded region. A sector with ...

Pick two points at random in a circular sector of radius 1 and central angle theta, and consider the length s of the line joining them. The following table summarizes ...

A circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...

Given two curves C_1 and C_2 and a fixed point O, let a line from O cut C_1 at Q and C_2 at R. Then the locus of a point P such that OP=QR is the cissoid. The word cissoid ...

The classification theorem of finite simple groups, also known as the "enormous theorem," which states that the finite simple groups can be classified completely into 1. ...

The extangents triangle is homothetic to the orthic triangle, and its homothetic center is known as the Clawson point, or sometimes the "crucial point." It has equivalent ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

Cluster analysis is a technique used for classification of data in which data elements are partitioned into groups called clusters that represent collections of data elements ...

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

The modulus of a complex number z, also called the complex norm, is denoted |z| and defined by |x+iy|=sqrt(x^2+y^2). (1) If z is expressed as a complex exponential (i.e., a ...