How long would it take you to calculate the area of this polygon?
Hopefully not too long.
But what about this one?
Pick’s Theorem offers an elegant formula that allows us to find the area of a lattice polygon – whether it be as simple as the former or as convoluted as the latter – in a matter of seconds. The theorem obviates the need to trudge through the tedious set of calculations that would otherwise be required to find the area of a polygon, and all we have to do is count the lattice points it encompasses.
Sounds easy enough, right?
Although the result itself is straightforward, proving that it holds for all polygons is anything but. Drawing from three classic papers on topics closely related to Pick’s Theorem, this presentation will take a deep dive into the intriguing foundations upon which Pick’s famous result is built.
Liu, Alex. “Lattice Points and Pick’s Theorem.” Mathematics Magazine 52.4 (1979): 232-235. JSTOR. Web. 31 August 2015.
Graver, Jack, and Yvette Monachino. “A Colorful Proof of Pick’s Theorem.” Math Horizons 18.2 (2010): 14-16. JSTOR. Web. 5 September 2015.
Funkenbusch, W.W. "From Euler's Formula to Pick's Formula Using an Edge Theorem." The American Mathematical Monthly 81.6 (1974): 647-648. JSTOR. Web. 31 August 2015.
Niven, Ivan, and H.S. Zuckerman. “Lattice Points and Polygonal Area.” The American Mathematical Monthly 74.10 (1967): 1195-1200. JSTOR. Web. 31 August 2015.
Math 450 Seminar Presents
"Primitive Triangles and Pick's Theorem
by: Charlie Michel
Tuesday, September 29, 1:40 p.m.
in Patterson 301
Come join us! All are welcome.