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A hypergeometric identity discovered by Ramanujan around 1910. From Hardy (1999, pp. 13 and 102-103), (1) where a^((n))=a(a+1)...(a+n-1) (2) is the rising factorial (a.k.a. ...

The set of points, known as boundary points, which are members of the set closure of a given set S and the set closure of its complement set. The boundary is sometimes called ...

The limit points of a set P, denoted P^'.

Let M^n be an n-manifold and let F={F_alpha} denote a partition of M into disjoint pathwise-connected subsets. Then if F is a foliation of M, each F_alpha is called a leaf ...

A discrete subset of R^s which is closed under addition and subtraction and which contains Z^s as a subset.

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

Given a convex plane region with area A and perimeter p, A-1/2p<N<=A+1/2p+1, where N is the number of enclosed lattice points (Nosarzewska 1948). This improves on Jarnick's ...

The use of percentages is a way of expressing ratios in terms of whole numbers. A ratio or fraction is converted to a percentage by multiplying by 100 and appending a ...

X subset= R^n is subanalytic if, for all x in R^n, there is an open set U and a bounded semianalytic set Y subset R^(n+m) such that X intersection U is the projection of Y ...

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...