Pick's Theorem

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

## No comments:

## Post a Comment