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Coverage of a square lattice by an inclined rectangle

Published online by Cambridge University Press:  01 July 2016

Dennis Rosen
Dennis Rosen*
Affiliation:
Birkbeck College, London
*
∗Postal address: Department of Crystallography, Birkbeck College, Malet Street, London, WC1E 7HX, UK.
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Abstract

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By use of a method of dissection, a formula is derived for the variance in the number of lattice points covered by a rectangle of arbitrary size, lying on a square lattice of unit spacing and inclined to the lattice at an angle of which the tangent is a rational fraction.

Keywords

GEOMETRIC PROBABILITYCOVERAGE
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 705 - 707
Copyright
Copyright © Applied Probability Trust 1989 

References

Kendall, M. and Moran, P. A. P. (1963) Geometrical Probability. Griffin, London.Google Scholar
Rosen, D. (1980) On the areas and boundaries of quantized objects. Comp. Graphics Image Proc. 13, 94–98.CrossRefGoogle Scholar