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The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

A Turing machine is a theoretical computing machine invented by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine consists of a ...

A definite integral is an integral int_a^bf(x)dx (1) with upper and lower limits. If x is restricted to lie on the real line, the definite integral is known as a Riemann ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

A d-dimensional discrete percolation model is said to be inhomogeneous if different graph edges (in the case of bond percolation models) or vertices (in the case of site ...

A state diagram is a labeled directed graph together with state information that can be used to indicate that certain paths on in a system may be traversed only in a certain ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

The shortest circular sequence of length sigma^n such that every string of length n on the alphabet a of size sigma occurs as a contiguous subrange of the sequence described ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...