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There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...

A cubic curve is an algebraic curve of curve order 3. An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a cycle polynomial whose coefficients are the numbers of cycles of ...

A cyclide is a pair of focal conics which are the envelopes of two one-parameter families of spheres, sometimes also called a cyclid. The cyclide is a quartic surface, and ...

The diamond graph is the simple graph on 4 nodes and 5 edges illustrated above (Brandstädt et al. 1987, p. 18). It is isomorphic to the complete tripartite graph K_(1,1,2) ...

The Dirac matrices are a class of 4×4 matrices which arise in quantum electrodynamics. There are a variety of different symbols used, and Dirac matrices are also known as ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...