Four bugs on a rectangle

S. J. Chapman; J. Lottes; L. N. Trefethen

doi:10.1098/rspa.2010.0506

Four bugs on a rectangle

S. J. Chapman, J. Lottes, L. N. Trefethen

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The 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.

Original language	English (US)
Pages (from-to)	881-896
Number of pages	16
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	467
Issue number	2127
DOIs	https://doi.org/10.1098/rspa.2010.0506
State	Published - Nov 10 2010
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: We 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1098/rspa.2010.0506

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title = "Four bugs on a rectangle",

abstract = "The 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 {\textcopyright} 2011 The Royal Society.",

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Four bugs on a rectangle

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