KAUST Grant NumberKUK-C1-013-04
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AbstractThe idealized mathematical problem of four bugs in cyclic pursuit starting from a 2-by-1 rectangle is considered, and asymptotic formulas are derived to describe the motion. In contrast to the famous case of four bugs on a square, here the trajectories quickly freeze to essentially one dimension. After the first rotation about the centre point, the scale of the configuration has shrunk by a factor of 10427907250, and this number is then exponentiated four more times with each successive cycle. Relations to Knuth's double-arrow notation and level-index arithmetic are discussed. This journal is © 2011 The Royal Society.
CitationChapman SJ, Lottes J, Trefethen LN (2010) Four bugs on a rectangle. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467: 881–896. Available: http://dx.doi.org/10.1098/rspa.2010.0506.
SponsorsWe have benefited from discussions with the other 2008 Problem Squad members Almut Eisentrager, Jen Pestana and Hao Wang. L.N.T. would also like to thank Mr and Mrs E. McLoughlin of Meols, Wirral, UK, for inviting him to a square dance shortly before this project began. This publication is based on work supported in part by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
PublisherThe Royal Society