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The volume of a lattice polyhedron

Published online by Cambridge University Press:  24 October 2008

I. G. Macdonald
I. G. Macdonald
Affiliation:
The University, Exeter
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Extract

Let L be the lattice of all points with integer coordinates in the real affine plane R2 (with respect to some fixed coordinate system). Let X be a finite rectilinear simplicial complex in R2 whose 0-simplexes are points of L. Suppose X is pure and the frontier Ẋ of X is a Jordan curve; then there is a well-known formula for the area of X in terms of the number of points of L which lie in X and Ẋ respectively, namely

where L(X) (resp. L(Ẋ)) is the number of points of L which lie in X (resp. Ẋ), and μ(X) is the area of X, normalized so that a fundamental parallelogram of L has unit area.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 4 , October 1963 , pp. 719 - 726
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

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