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An equation of the form y=ax^3+bx^2+cx+d, (1) where the three roots of the equation coincide (and are therefore real), i.e., y=a(x-r)^3=a(x^3-3rx^2-3r^2x-r^3). (2) Loomis ...

A regular skew polyhedron is a polyhedron whose faces and vertex figures are regular skew polygons. There are only three regular skew polyhedra in Euclidean three-space ...

Truncation is the removal of portions of solids falling outside a set of symmetrically placed planes. The operation implemented as Truncate[polyhedron, r] in the Wolfram ...

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

A class formed by sets in R^n which have essentially the same structure, regardless of size, shape and dimension. The "essential structure" is what a set keeps when it is ...

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, ...

Abstract Algebra

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

A topology induced by the metric g defined on a metric space X. The open sets are all subsets that can be realized as the unions of open balls B(x_0,r)={x in X|g(x_0,x)<r}, ...

The class m, curve order n, number of ordinary double points delta, number of cusps kappa, number of inflection points (inflection points) iota, number of bitangents tau, and ...