Difference between revisions of "Pick's Theorem"

 
(Pick's Theorem)
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== Pick's Theorem ==
 
  
 
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:

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

with $I$ being the number of interior lattice points, and $B$ being the number of lattice points on the boundary.

Proof

some one edit one in please...