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A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

The second knot polynomial discovered. Unlike the first-discovered Alexander polynomial, the Jones polynomial can sometimes distinguish handedness (as can its more powerful ...

A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

The cuboctahedron, also called the heptaparallelohedron or dymaxion (the latter according to Buckminster Fuller; Rawles 1997), is the Archimedean solid with faces 8{3}+6{4}. ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

A Tschirnhausen transformation can be used to algebraically transform a general quintic equation to the form z^5+c_1z+c_0=0. (1) In practice, the general quintic is first ...

The Burridge-Knopoff model is a system of differential equations used to model earthquakes using n points on a straight line, each of mass m, that interact with each other ...

All closed surfaces, despite their seemingly diverse forms, are topologically equivalent to spheres with some number of handles or cross-caps. The traditional proof follows ...

A diagonal matrix D=diag(d_1,...,d_n) sometimes also called the valency matrix corresponding to a graph that has the vertex degree of d_i in the ith position (Skiena 1990, p. ...

A Euclidean number is a number which can be obtained by repeatedly solving the quadratic equation. Euclidean numbers, together with the rational numbers, can be constructed ...