Organizers: Timothy Goldberg, Lenoir-Rhyne University (timothy.goldberg@gmail.com); ron taylor, Berry College (rtaylor@berry.edu)
“Recreational mathematics is inspired by deep ideas that are hidden in puzzles, games, and other forms of play.” (Robert Vallin, quoted in “Three New SIGMAAs Formed”, by Jacqueline Jensen-Vallin, MAA Focus Vol. 38, No. 2, April/May 2018.) The field of recreational math includes a startling variety of mathematical ideas and strategies, and tends to be especially entertaining and accessible. (And they make wonderful examples and research projects for students!) This session is devoted to talks related to recreational math, in any of its myriad forms!
EvenQuads is a SET-like card game published by the AWM whose goal is to find “quads”, which are sets of four cards satisfying a particular pattern. The cards can be viewed as points in the finite affine geometry AG(6,2), and a quad in the card game corresponds to a plane in AG(6,2). We are most interested in quad-free collections of cards, which turn out to be Sidon Sets. We will describe an analog of the "Cap Set problem" for EvenQuads, and discuss known results. In particular, we will address the question of how many cards you must lay down to guarantee a quad.
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The Central Limit Theorem is one of the most fundamental principles in probability, stating that the probability distribution of the average of independent measurements of the same random variable has the ubiquitous bell curve as a limit as the sample size increases. This talk will use different numbers of fair dice to explore this convergence as one of the easiest examples of that convergence if not the quickest.
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This talk will focus on an initiative at Mars Hill University for co-curricular math exploration. Math faculty members use problems, activities, and puzzles from Math Circles to engage with students outside of the lecture classroom. The ideas used in the activities are applications that students would not necessarily encounter in the classroom but allow for exploration with patterns, strategies for games, and recognition of mathematics in everyday life. A large emphasis of the initiative is for students to realize that math can be fun!
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In this session, I will describe how I introduce fractal mathematics with iterative processes and focus on key aspects of the golden ratio and transcendental number Phi. I will include some of the video clips I use to get students engaged with the concepts, examples they practice in the classroom to further their understanding, and assignments that align with the learning objectives of this course - “Students will craft written and/or oral communication demonstrating organization, clarity, logic and skill for various audiences.”
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Proof lies at the heart of mathematical reasoning, yet teaching proof in a liberal arts mathematics course poses a unique challenge. How can we showcase the power and utility of axiomatic reasoning while keeping the content accessible to students from diverse majors and backgrounds? A simple game involving blue and red poker chips can offer the perfect balance of accessibility and depth, inviting students to explore axiomatic reasoning in an engaging yet rigorous way. With just three axioms, students can discover hidden structures within the game and even determine their optimal next moves. We will introduce the game and its axioms, and then we will discuss how it can be used as a classroom activity to demonstrate the elegance of mathematical proof through play.
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Quad-128 is a game played with two distinguishable Quad-64 decks; for example, each deck has a different background color. The game play is similar, but the combined deck is now a model for the affine geometry
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Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a position that the players take turns changing in defined ways or moves to achieve a defined winning condition. In this talk, I will present some ideas about the structural properties of a combinatorial game - in particular, the subtraction game.
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Temari is a traditional Japanese fiber art in which designs are stitched to the surface of a ball. Many Temari designs begin with a geometric partition of the sphere. Temari designs can be viewed through the lens of recreational math as it is a leisure art with mathematical properties. In this presentation, I will first describe a standard procedure for partitioning Temari balls. I will then demonstrate application of this procedure to difference surfaces. Finally, I will compare the results to standard mathematical projections, such as stereographic and cylindrical projections.
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A Tangle is a smooth closed curve formed by the union of arcs of congruent circles, known as links. We use the Gauss-Bonnet theorem to prove an interesting result about the number of concave v. convex links in a Tangle. This in turn allows us to show that all "triangular Tangles" (planar Tangles formed from sixths of circles) may be constructed by a sequence of fundamental operations starting from a circle.
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