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Mathematics and Statistics Colloquium: Michael Jones

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Thursday, February 9, 2023 4pm

27 Graves Place, Holland, MI 49423-3617

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“On Euclid's Game: The Fractal Structure of Losing Positions in the Calkin-Wilf Tree” by Michael Jones, PhD Introduced by Cole and Davie in 1969, Euclid is a combinatorial game based on the operations of the Euclidean algorithm. Using high-school geometry, I'll prove Cole and Davie's result that describes which player should win under optimal play and how this depends on the Golden Ratio. After reviewing how the Calkin-Wilf tree provides an enumeration of the positive rational numbers, I will explain how game play moves along the branches of the Calkin-Wilf tree.  Finally, I will prove that the arrangement of the losing positions in the tree form a fractal. All of the necessary mathematics to understand the talk will be developed during the talk. This work is joint with Brittany Ohlinger from Albright College.

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