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A rolling polyhedron graph is a graph obtained by rolling a polyhedral solid along a board whose tiles match up with the faces of the polyhedron being rolled. The vertices of ...

The Smale horseshoe map consists of a sequence of operations on the unit square. First, stretch in the y direction by more than a factor of two, then compress in the x ...

A trapezoid is a quadrilateral with two sides parallel. The trapezoid is equivalent to the British definition of trapezium (Bronshtein and Semendyayev 1977, p. 174). An ...

Any two rectilinear figures with equal area can be dissected into a finite number of pieces to form each other. This is the Wallace-Bolyai-Gerwien theorem. For minimal ...

An array is a "list of lists" with the length of each level of list the same. The size (sometimes called the "shape") of a d-dimensional array is then indicated as ...

The Buffon-Laplace needle problem asks to find the probability P(l,a,b) that a needle of length l will land on at least one line, given a floor with a grid of equally spaced ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

The angular twist theta of a shaft with given cross section is given by theta=(TL)/(KG) (1) (Roark 1954, p. 174), where T is the twisting moment (commonly measured in units ...

Turmites, also called turning machines, are 2-dimensional Turing machines in which the "tape" consists of a grid of spaces that can be written and erased by an active ...

The one-dimensional wave equation is given by (partial^2psi)/(partialx^2)=1/(v^2)(partial^2psi)/(partialt^2). (1) In order to specify a wave, the equation is subject to ...