Difference between revisions of "Pick's Theorem"

(it's a theorem. ;))
Line 1: Line 1:
 +
{{WotWAnnounce|week=September 11- September 18}}
 +
 
'''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:
 
'''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:
  

Revision as of 00:30, 14 September 2008

This is an AoPSWiki Word of the Week for September 11- September 18

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 though it is less powerful it is a good tool to have in solving problems.


An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.


Proof

This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS