Pick's Theorem: Difference between revisions
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Pick's theorem expresses the area of a polygon with all its vertices on [[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: | Pick's theorem expresses the area of a polygon with all its vertices on [[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: | ||
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with <math>I</math> being the number of interior lattice points, and <math>B</math> being the number of lattice points on the boundary. | with <math>I</math> being the number of interior lattice points, and <math>B</math> being the number of lattice points on the boundary. | ||
== Proof == | == Proof == | ||
some one edit one in please... | some one edit one in please... | ||
Revision as of 19:11, 4 November 2006
Pick's theorem expresses the area of a polygon with all its vertices on 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:
with 
being the number of interior lattice points, and 
being the number of lattice points on the boundary.
Proof
some one edit one in please...
