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A merge sort (or collation sort) is the combination of two or more ordered lists into a single ordered list (Knuth 1998, p. 158). Merge sorting was one of the first methods ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

There appears to be no term in standard use for a graph with graph crossing number 1. Furthermore, the terms "almost planar" and "1-planar" are used in the literature for ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

The conchoid of de Sluze is the cubic curve first constructed by René de Sluze in 1662. It is given by the implicit equation (x-1)(x^2+y^2)=ax^2, (1) or the polar equation ...

An oval dissected into pieces which are to used to create pictures. The resulting figures resemble those constructed out of tangrams.

The cyclocevian triangle DeltaA^('')B^('')C^('') of a reference triangle DeltaABC with respect to a point P is the triangle formed by the vertices determined by the ...

The Dürer folium is a special case of the rose curve with n=1. It is therefore also an epitrochoid. It has polar equation r=asin(theta/2) (1) and can be written as a ...

The pedal curve of an ellipse with parametric equations x = acost (1) y = bsint (2) and pedal point (x_0,y_0) is given by f = ...

The pedal curve of a rectangular hyperbola with the pedal point at the focus is a circle (left figure; Hilbert and Cohn-Vossen 1999, p. 26). The pedal curve of a rectangular ...