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The Ergodic Theory Carnival
Julia Barnes and Lorelei Koss
Vol. 83, No. 3 (June 2010), pp. 180-190
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/002557010x494823
Page Count: 11
You can always find the topics here!Topics: Taffies, Carousels, Mathematical functions, Clowns, Children, Ergodic theory, Carnivals, Lebesgue measures, Mathematical intervals, Mathematics
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SummaryThe Birkhoff ergodic theorem, proved by George David Birkhoff in 1931, allows us to investigate the long-term behavior of certain dynamical systems. In this article, we explain what it means for a function to be ergodic, and we present Birkhoff’s theorem. We construct models of activities typically found at carnivals and compare and contrast them by analyzing their ergodic theory properties. We use these carnival models to show how Birkhoff’s ergodic theorem can be used to help a photographer set up her equipment to take pictures of all children on a carousel and to aid a magician in finding a lost jewel in a sticky mess of taffy.
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