Strachan, I.A.B.
(2003)
How to count curves: from nineteenth-century problems to twenty-first-century solutions.
*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, 361(1813),
pp. 2633-2647.
(doi: 10.1098/rsta.2003.1261)

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Publisher's URL: http://dx.doi.org/10.1098/rsta.2003.1261

## Abstract

Find the next term in the sequence 1, 1, 12, 620, 87304. This particular problem belongs to a branch of mathematics called enumerative geometry. This is concerned with curve–counting – counting the number of curves that can be drawn on a particular geometric object. The sequence above is easy to describe: each term represents the number of curves, with increasing complexity, one can draw though a certain number of points on a plane. Despite its simplicity, the problem remained unsolved for most of the twentieth century. The solution – a formula with which one may calculate any term in the series – was discovered only in the century's closing decade. This article will describe the above problem, and some of the unexpected mathematics and physics that was used in finding its solution.

Item Type: | Articles |
---|---|

Status: | Published |

Refereed: | Yes |

Glasgow Author(s) Enlighten ID: | Strachan, Professor Ian |

Authors: | Strachan, I.A.B. |

Subjects: | Q Science > QA Mathematics |

College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |

Journal Name: | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Publisher: | Royal Society |

ISSN: | 1364-503X |

ISSN (Online): | 1471-2962 |

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