Difference between revisions of "Pick's Theorem"

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where <math>I</math> is the number of lattice points in the interior and <math>B</math> being the number of lattice points on the boundary.
 
where <math>I</math> is the number of lattice points in the interior and <math>B</math> being the number of lattice points on the boundary.
It is similar to the shoestring formula, and though it is less powerful it is a good tool to have in solving problems.
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It is similar to the shoestring formula, and although it is less powerful it is a good tool to have in solving problems.
  
 
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Revision as of 17:01, 28 July 2010

Pick's Theorem expresses the area of a polygon, all of whose vertices are lattice points in a coordinate plane, in terms of the number of lattice points inside the polygon and the number of lattice points on the sides of the polygon. The formula is:

$A = I + \frac{B}{2} - 1$

where $I$ is the number of lattice points in the interior and $B$ being the number of lattice points on the boundary. It is similar to the shoestring formula, and although it is less powerful it is a good tool to have in solving problems.


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Proof

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