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CATEGORIES:Academics,Natural & Applied Sciences Division,Mathematics and St
atistics
DESCRIPTION:“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 Euc
lidean algorithm. Using high-school geometry\, I'll prove Cole and Davie's
result that describes which player should win under optimal play and how th
is depends on the Golden Ratio. After reviewing how the Calkin-Wilf tree pr
ovides an enumeration of the positive rational numbers\, I will explain how
game play moves along the branches of the Calkin-Wilf tree. Finally\, I w
ill prove that the arrangement of the losing positions in the tree form a f
ractal. All of the necessary mathematics to understand the talk will be dev
eloped during the talk. This work is joint with Brittany Ohlinger from Albr
ight College.
DTEND:20230209T220000Z
DTSTAMP:20240714T021150Z
DTSTART:20230209T210000Z
GEO:42.787588;-86.106797
LOCATION:VanderWerf Hall\, 104
SEQUENCE:0
SUMMARY:Mathematics and Statistics Colloquium: Michael Jones
UID:tag:localist.com\,2008:EventInstance_42304817065780
URL:https://calendar.hope.edu/event/mathematics_and_statistics_colloquium_m
ichael_jones
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