Math 450 Presents "Fractals and Mysterious Triangles"

Cards of three colors are dealt in a row of size n. The cards are then continually dealt into rows above each other of size n-1, n-2, n-3, … until the row of size 1 is reached. The cards must be placed following 2 rules. One, if two cards, adjacent cards, from the previous row share the same color, the card above them must be that color as well. Two, if two adjacent cards are different colors, the card above them must be of the third color. These cards form a “mysterious triangle.” We want to know how we could predict the color of the apex card of the triangle without dealing out all the cards. Using Sierpinski Triangles, mod 3 arithmetic, and fractals, we will figure out exactly that.

Jones, M. A., Mitchell, L., Shelton, B. “Fractals and Mysterious Triangles.” Math Horizons.

      September 2015. pp 22-25.

 

Math 450 Presents

"Fractals and Mysterious Triangles"

by: Shelbey Linder

Tuesday, October 20, 2015, 1:40 p.m.

in Patterson 301

 

Come join us! All are welcome.



Math 450 Seminar Presents "Mathematics for Gamers!"

The problem discussed in this article begins with the introduction of zombies in the video game Call of Duty: Black Ops. However, the solution to this problem is a mathematical problem that needs a solution as well. There are four dials placed among four levels of a building, and the solution of this problem requires a certain algorithm of turning the dials to read in order 2, 7, 4, and 6.

In Math Horizons, February 2014 edition, Heidi Hulsizer tackles the problem presented to her in one of the video games she plays regularly. After careful consideration she discovered two ways to mathematically solve this Easter egg. The first way is with an algebraic approach, while the second deals with a matrix approach.  Who knew video games involved so much thinking!

Math 450 Presents

"Mathematics for Gamers!"

by: Jacob Ackerman

Tuesday, October 13, 2015, 1:40 p.m.

in Patterson 301

Come join us! All are welcome.

Math 450 Seminar Presents "The Multiplication Game!"

The game is simple, the dealer hands you a random number that you cannot see, and you then enter your own integer. If the first digit of the product is between 4 and 9 you win! If the first digit of the product is 1, 2, or 3 the dealer wins. The odds seem tempting, would you take them?

In an article from the April 2010 edition of Mathematics Magazine, Kent E. Morrison analyzes this game and discovers what the odds are and how we need to apply game theory to the problem in order to completely solve the total expected outcome of this game. Although this may seem like a very straight forward problem, we will learn that a lot goes into solving this simple multiplication game.

 

Math 450 Seminar Presents

"The Multiplication Game"

by: Alexander Lillich

Tuesday, October 6, 2015, 1:40 p.m.

in Patterson 301

 

Come join us! All are welcome.



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!