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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 ...

Let S be a set of simple polygonal obstacles in the plane, then the nodes of the visibility graph of S are just the vertices of S, and there is an edge (called a visibility ...

Complex Analysis

Differential Geometry

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...