Pick's Theorem was first published in 1899 by Georg Alexander Pick. The theorem gives an
important formula for the area of lattice polygons.
A geoboard is a good way to explore these lattice polygons. A geoboard is a piece of wood
or board with pegs or nails arranged in a regular grid. The board represents a section of the
plane and the pegs or nails are the lattice points. Children can stretch rubber bands over the
lattice points to create polygons.
These strange shapes above are examples of lattice polygons, which is a polygon whose lies
on points in the plane that have integral coordinates.
How to calculate its area?
By simply counting the lattice points! Count the number of lattice points on the boundary of the
polygon (b) and the number of lattice points inside the polygon (i), then the area (A) of the
polygon is given by Pick's Theorem
Area (A) = i +(b/2) - 1
What will children learn from this activity?
Children will learn
1) to look at the number relationships to determine Pick's theorem
2) to use this theorem to predict the area of more complex shapes