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A visual approach to some elementary number theory
Published online by Cambridge University Press: 01 August 2016
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Euclidean geometry and fractions not only make unlikely bedfellows, but would seem to be a sure recipe for boredom. However, in this paper, with the help of a little history, we hope to prove the opposite.
Given a (rectangular) lattice, then a lattice polygon is a polygon whose vertices are lattice points. Pick's theorem [1] - the area of a simple lattice polygon is given by ½b + i – 1 where b is the number of lattice points on the boundary of the polygon, and i is the number in its interior – is well known and has been proved many times and in many ways.
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