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A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices. The spherical triangle is the ...

A maximum clique of a graph G is a clique (i.e., complete subgraph) of maximum possible size for G. Note that some authors refer to maximum cliques simply as "cliques." The ...

A hexagon (not necessarily regular) on whose polygon vertices a circle may be circumscribed. Let sigma_i=Pi_i(a_1^2,a_2^2,a_3^2,a_4^2,a_5^2,a_6^2) (1) denote the ith-order ...

A problem in game theory first discussed by A. Tucker. Suppose each of two prisoners A and B, who are not allowed to communicate with each other, is offered to be set free if ...

Any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal grid (i.e., the honeycomb, illustrated above). Pappus refers to the ...

Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded ...

An odd alternating permutation number, more commonly called an Euler number or secant number.

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

An identity in calculus of variations discovered in 1868 by Beltrami. The Euler-Lagrange differential equation is (partialf)/(partialy)-d/(dx)((partialf)/(partialy_x))=0. (1) ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...