PSG Solution Published in School Science and Mathematics, April 2015

The Problem Solving Group (PSG) at Ashland University's Math and Computer Science Department, submitted 4 problems last year. They received acknowledgement for 3 correct solutions and their solution to Problem 5332 from School Science and Mathematics website (April 2015) was selected to be published.

Congratulations, PSG!

Come and be a part of the Problem Solving Group (PSG) group.

Math 450 Seminar Presents "Primitive Triangles and Pick's Theorem"

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.

Alumni News

Caitlin Music '13 completed the two year Master of Statistics program at Miami University. She started her career at AcuSport in Bellefontaine, OH. She is a Supply Planning Analyst. In this position, she is responsible for analyzing POS data and providing insight into inventory, fill rate, etc. Join the Math/CS department in congratulating Caitlin on her success.

Problem Solving Group

The Problem Solving Group's first meeting is Tuesday, September 22, at 7:00 p.m. in Patterson 324.  PSG will meet Bi-Weekly at 7:00 p.m. in Patterson 324. Call Dr. Chris Swanson for details.

Come Join Us! We look forward to seeing you there!

Math 450 Senior Seminar Presents "Colorful Symmetries"

Quiz!!

                1. How many ways can you paint your fingernails with three different colors?

                      2. How many ways are there to color a disk divided into three equal parts with one of two                                                       colors per section?

                      3. How many ways can you color an icosahedron with one of n colors per face?

       

      Asking simple questions that are difficult to answer is common in mathematics. The first question seems pretty straight forward. Yet the second requires a bit more understanding, one of basic geometry, group theory and combinatorics.

     

      Using Burnside’s Lemma, sometimes, called the orbit-counting theorem, we will explore this question and others like it, considering the much needed rotation of an object, looking at it from all sides.

  

      By solving a much simpler problem, we will build to the question of the icosahedron, showing with the proper ‘tools’, the problem-solving approach needed is not that hard after all.

Bargh, B. Chase, J. Wright, M. (2014). Colorful Symmetries. Math Horizons, April 2014, pp 14-17

Math 450 Senior Seminar Presents

"Colorful Symmetries"

by: Brenda Forbes

Tuesday, September 22, 1:40 p.m.

in Patterson 301

Math 450 Senior Seminar Presents "Evaluating Risk in the Board Game 'Risk'"

In the board game RISK, players attempt to conquer the world by capturing all territories on the board, with battle outcomes determined by dice rolls. Let A be the number of attacking armies and D be the number of defending armies in two adjacent territories. This talk will present the probability the defending territory will be captured and the expected number of armies lost by the attacking territory in the capture.

Math 450 Senior Seminar Presents

"Evaluating Risk in the Board Game Risk"

by: Dr. Christopher N. Swanson

Tuesday, September 15, 1:40 p.m.

in Patterson 301