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Let j_k(alpha) denote the number of cycles of length k for a permutation alpha expressed as a product of disjoint cycles. The cycle index Z(X) of a permutation group X of ...

A cyclic pentagon is a not necessarily regular pentagon on whose polygon vertices a circle may be circumscribed. Let such a pentagon have edge lengths a_1, ..., a_5, and area ...

The polar curve r=1+2cos(2theta) (1) that can be used for angle trisection. It was devised by Ceva in 1699, who termed it the cycloidum anomalarum (Loomis 1968, p. 29). It ...

The Darboux cubic Z(X_(20)) of a triangle DeltaABC is the locus of all pedal-cevian points (i.e., of all points whose pedal triangle is perspective with DeltaABC). It is a ...

A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as ...

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

A set A in a first-countable space is dense in B if B=A union L, where L is the set of limit points of A. For example, the rational numbers are dense in the reals. In ...

Also known as "Laplacian" determinant expansion by minors, expansion by minors is a technique for computing the determinant of a given square matrix M. Although efficient for ...

The term diamond is another word for a rhombus. The term is also used to denote a square tilted at a 45 degrees angle. The diamond shape is a special case of the superellipse ...

Differential algebra is a field of mathematics that attempts to use methods from abstract algebra to study solutions of systems of polynomial nonlinear ordinary and partial ...