Difference between revisions of "Pick's Theorem"
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| − | + | '''Pick's Theorem''' expresses the [[area]] of a [[polygon]], all of whose [[vertex | 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: | |
| − | + | <math>A = I + \frac{B}{2} - 1</math> | |
| − | <math> | + | 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. |
| − | + | {{image}} | |
== Proof == | == Proof == | ||
| − | + | {{stub}} | |
Revision as of 14:56, 5 November 2006
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:
where 
is the number of lattice points in the interior and 
being the number of lattice points on the boundary.
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Proof
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