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Let H be a Hilbert space and M a closed subspace of H. Corresponding to any vector x in H, there is a unique vector m_0 in M such that |x-m_0|<=|x-m| for all m in M. ...

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

The Gömböc (meaning "sphere-like" in Hungarian) is the name given to a class of convex solids which possess a unique stable and a unique unstable point of equilibrium. ...

A type of number involving the roots of unity which was developed by Kummer while trying to solve Fermat's last theorem. Although factorization over the integers is unique ...

The midcircle of two given circles is the circle which would invert the circles into each other. Dixon (1991) gives constructions for the midcircle for four of the five ...

Given a real number q>1, the series x=sum_(n=0)^inftya_nq^(-n) is called the q-expansion, or beta-expansion (Parry 1957), of the positive real number x if, for all n>=0, ...

There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

Let a graph G=(V,E) be defined on vertex set V and edge set E. Then a construction sequence (or c-sequence) for G is a linear order on V union E in which each edge appears ...

The phrase dependent percolation is used in two-dimensional discrete percolation to describe any general model in which the states of the various graph edges (in the case of ...