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A species of structures is a rule F which 1. Produces, for each finite set U, a finite set F[U], 2. Produces, for each bijection sigma:U->V, a function F[sigma]:F[U]->F[V]. ...

Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for vector addition of two or more ...

WireWorld is a two-dimensional four-color cellular automaton introduced by Brian Silverman in 1987. The rule for the automaton uses the cell's old value a together with the ...

A theorem giving a criterion for an origami construction to be flat. Kawasaki's theorem states that a given crease pattern can be folded to a flat origami iff all the ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

Bowling, known as "ten pins" throughout most of the world, is a game played by rolling a heavy ball down a long narrow track and attempting to knock down ten pins arranged in ...

A Turing machine which, by appropriate programming using a finite length of input tape, can act as any Turing machine whatsoever. In his seminal paper, Turing himself gave ...

The tangent space at a point p in an abstract manifold M can be described without the use of embeddings or coordinate charts. The elements of the tangent space are called ...