This assignment is pretty simple. Write up our discussion of Pick’s Theorem. Try to explain exactly what the theorem says. Define the function K where K(a) = (number of interior lattice points of a) + ½ (number of boundary lattice points) – 1. Define the function A where A(a) = area of a. Explain Pick’s Theorem for a rectangle R. Explain the additivity formula: K(a + b) = K(a)+K(b). Explain how Pick’s theorem is then proved for right-triangles, arbitrary triangles, and finally for more general lattice polygons. Make sure to give some examples of lattice polygons where Pick’s theorem does not hold.

You might want to visit the Web site: http://www.cut-the-knot.org/ctk/Pick.shtml and/or do a search on “Pick’s Theorem.”