### 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.**

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