Pick’s Theorem

Austrian mathematician Georg Pick first stated this theorem in 1899. However it wasn’t brought to broad attention until 1969. In this exploration, participants will use rates of change to aid them in discovering Pick’s famous formula by finding a relationship between the area of the figure, the number of perimeter pegs, and the number of interior pegs. This session is also suitable for student circles or the classroom.

Additional Inspiration

J. E. Reeve, On the Volume of Lattice Polyhedra, Proceedings of the London Mathematical Society, s37(1):378395

Pick, Georg (1899). Geometrisches zur Zahlenlehre. Sitzungsberichte des deutschen naturwissenschaftlich-medicinischen Vereines fr Bhmen ”Lotos” in Prag. (Neue Folge) 19: 311-319