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An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...

A variable is a symbol on whose value a function, polynomial, etc., depends. For example, the variables in the function f(x,y) are x and y. A function having a single ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

von Neumann-Bernays-Gödel set theory (abbreviated "NBG") is a version of set theory which was designed to give the same results as Zermelo-Fraenkel set theory, but in a more ...

There are many mathematical and recreational problems related to folding. Origami, the Japanese art of paper folding, is one well-known example. It is possible to make a ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

Bridge is a card game played with a normal deck of 52 cards. The number of possible distinct 13-card hands is N=(52; 13)=635013559600, (1) where (n; k) is a binomial ...

The Brouwer-Haemers graph is the unique strongly regular graph on 81 vertices with parameters nu=81, k=20, lambda=1, mu=6 (Brouwer and Haemers 1992, Brouwer). It is also ...

Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...