Four bugs on a rectangle
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. Af...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1797106001414979584 |
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| author | Chapman, S Lottes, J Trefethen, L |
| author_facet | Chapman, S Lottes, J Trefethen, L |
| author_sort | Chapman, S |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T06:55:28Z |
| format | Journal article |
| id | oxford-uuid:fe00ca81-2ee4-4f7e-aeb5-e08e32f9e3f9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:55:28Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:fe00ca81-2ee4-4f7e-aeb5-e08e32f9e3f92022-03-27T13:32:54ZFour bugs on a rectangleJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fe00ca81-2ee4-4f7e-aeb5-e08e32f9e3f9EnglishSymplectic Elements at Oxford2011Chapman, SLottes, JTrefethen, LThe 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. |
| spellingShingle | Chapman, S Lottes, J Trefethen, L Four bugs on a rectangle |
| title | Four bugs on a rectangle |
| title_full | Four bugs on a rectangle |
| title_fullStr | Four bugs on a rectangle |
| title_full_unstemmed | Four bugs on a rectangle |
| title_short | Four bugs on a rectangle |
| title_sort | four bugs on a rectangle |
| work_keys_str_mv | AT chapmans fourbugsonarectangle AT lottesj fourbugsonarectangle AT trefethenl fourbugsonarectangle |