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A sutured manifold is a tool in geometric topology which was first introduced by David Gabai in order to study taut foliations on 3-manifolds. Roughly, a sutured manifold is ...

A median A_1M_1 of a triangle DeltaA_1A_2A_3 is the Cevian from one of its vertices A_1 to the midpoint M_1 of the opposite side. The three medians of any triangle are ...

Fermat's last theorem is a theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The ...

A folding function is a function that maps the integers Z={...,-3,-2,-1,0,1,2,3,...} onto the nonnegative integers Z^*={0,1,2,3,...}. This type of function arises naturally ...

A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of ...

There are two different statements, each separately known as the greatest common divisor theorem. 1. Given positive integers m and n, it is possible to choose integers x and ...

A graceful graph is a graph that can be gracefully labeled. Special cases of graceful graphs include the utility graph K_(2,3) (Gardner 1983) and Petersen graph. A graph that ...

Guy's "strong law of small numbers" states that there aren't enough small numbers to meet the many demands made of them. Guy (1988) also gives several interesting and ...

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 ...

A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...