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A polyhedral graph corresponding to the skeleton of a Platonic solid. The five platonic graphs, the tetrahedral graph, cubical graph, octahedral graph, dodecahedral graph, ...

A rational amicable pair consists of two integers a and b for which the divisor functions are equal and are of the form sigma(a)=sigma(b)=(P(a,b))/(Q(a,b))=R(a,b), (1) where ...

Let psi_1(x) and psi_2(x) be any two real integrable functions in [a,b], then Schwarz's inequality is given by |<psi_1|psi_2>|^2<=<psi_1|psi_1><psi_2|psi_2>. (1) Written out ...

Sphere line picking is the selection of pairs of points corresponding to vertices of a line segment with endpoints on the surface of a sphere. n random line segments can be ...

The ten-of-diamonds decahedron is a stereohedron and space-filling polyhedron on 8 vertices, 16 edges, and 10 faces (8 of which are non-equilateral triangles and two of which ...

Consider the solid enclosed by the three hyperboloids specified by the inequalities x^2+y^2-z^2 <= 1 (1) y^2+z^2-x^2 <= 1 (2) z^2+x^2-y^2 <= 1. (3) This work dubs this solid ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, ...

An n-mark Golomb ruler is a set of n distinct nonnegative integers (a_1,a_2,...,a_n), called "marks," such that the positive differences |a_i-a_j|, computed over all possible ...

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...