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SUMMARY:Claire Merriman (Ohio State University)
DTSTART:20210105T133000Z
DTEND:20210105T143000Z
DTSTAMP:20260423T021450Z
UID:OWNS/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/28/">$\
 \alpha$-odd continued fractions</a>\nby Claire Merriman (Ohio State Univer
 sity) as part of One World Numeration seminar\n\n\nAbstract\nThe standard 
 continued fraction algorithm come from the Euclidean algorithm. We can als
 o describe this algorithm using a dynamical system of $[0\,1)$\, where the
  transformation that takes $x$ to the fractional part of $1/x$ is said to 
 generate the continued fraction expansion of $x$. From there\, we ask two 
 questions: What happens to the continued fraction expansion when we change
  the domain to something other than $[0\,1)$? What happens to the dynamica
 l system when we impose restrictions on the continued fraction expansion\,
  such as finding the nearest odd integer instead of the floor? This talk w
 ill focus on the case where we first restrict to odd integers\, then start
  shifting the domain $[\\alpha-2\, \\alpha)$.\n \nThis talk is based on jo
 int work with Florin Boca and animations done by Xavier Ding\, Gustav Jenn
 etten\, and Joel Rozhon as part of an Illinois Geometry Lab project.\n
LOCATION:https://researchseminars.org/talk/OWNS/28/
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