Cikojević, Monika
(2015)
*Fermat-Steinerov problem.*
Diploma thesis, Faculty of Science > Department of Mathematics.

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## Abstract

The Fermat-Steiner problem is a classical mathematical problem which numerous mathematicians have dealt with since the 17th century. The gist of the problem is determining such a point in the plane of a given triangle, so that the sum of the distances between that point and the vertices of the triangle is minimal. It is interesting that the solution can be found by completely different approaches, from purely geometric, by using calculus and by using practical mechanical method in which minimum energy principle is used. Motivation for the basic and weighted problem can be found in its usage for different optimization tasks, e.g. three villages or three factories. The Fermat-Steiner point, which is the solution of the problem, can be geometrically characterized in various interesting ways. Furthermore, the inverse problem of the weighted Fermat-Steiner problem is considered, in which it is investigated whether there exist such weights that a given point is the solution of the weighted problem. We have put forward various different proofs in order to show the historical development of the approach to the problem, and its generalizations. In that way we also wanted to show the beauty and diversity of mathematical thought.

Item Type: | Thesis (Diploma thesis) |
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Supervisor: | Šiftar, Juraj |

Date: | 2015 |

Number of Pages: | 36 |

Subjects: | NATURAL SCIENCES > Mathematics |

Divisions: | Faculty of Science > Department of Mathematics |

Depositing User: | Iva Prah |

Date Deposited: | 07 Oct 2015 09:09 |

Last Modified: | 07 Oct 2015 09:09 |

URI: | http://digre.pmf.unizg.hr/id/eprint/4253 |

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