Pick’s Theorem

This formula was created by Georg Alexander Pick in 1899.

 

Using the Geoboard to Assist :

 

·        Draw a polygon on the Geoboard

·        Determine the number of boundary points and the number of interior points and calculate its area

·        Repeat with different polygons

·        Draw polygons without any interior points and find the area

·        Draw polygons with one interior point and find the area

·        Draw polygons with two interior points and find the area

·        Prepare a table with number of boundary points, number of interior points, and area. Discover that the relationship between B the number of boundary points, i the number of internal points, and the area of the geoboard polygon is given by Pick's formula A = I + ½ B – 1

 

The diagram below explains this further.

 

I understand this better now! Wow :)

Marina Ho
BSc08