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The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

A doubly stochastic matrix is a matrix A=(a_(ij)) such that a_(ij)>=0 and sum_(i)a_(ij)=sum_(j)a_(ij)=1 is some field for all i and j. In other words, both the matrix itself ...

A number of attractive tetrahedron 10-compounds can be constructed. The first (left figures) can be obtained by combining tetrahedron 5-compounds of opposite chirality ...

A bubble is a minimal-energy surface of the type that is formed by soap film. The simplest bubble is a single sphere, illustrated above (courtesy of J. M. Sullivan). More ...

The constant e^pi that Gelfond's theorem established to be transcendental seems to lack a generally accepted name. As a result, in this work, it will be dubbed Gelfond's ...

The Gosset graph is a 27-regular graph on 56 vertices which is the skeleton of the Gosset polytope 3_(21). It is a distance-regular graph with intersection array ...

The Legendre symbol is a number theoretic function (a/p) which is defined to be equal to +/-1 depending on whether a is a quadratic residue modulo p. The definition is ...

A minimum vertex cover is a vertex cover having the smallest possible number of vertices for a given graph. The size of a minimum vertex cover of a graph G is known as the ...

The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...