Kromjong, G.L.P. (2013) Every knot is a billiard knot. Bachelor's Thesis, Mathematics.
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Abstract
In this article we study Daniel Pecker’s proof of the theorem saying that for an ellipse E (which is not a circle) and an elliptic cylinder D=Ex[0,1] it can be stated that every knot/link is a billiard knot/link. To understand the proof first billiard trajectories in an ellipse, Jacobian elliptic functions and Poncelet polygons must be introduced. Then there are some statements preceding the main theorem, containing the famous Poncelet’s closure theorem, the irregularity of Poncelet odd polygons and Kronecker’s density theorem. In the final proof both the situation of knots and the situation of links will be considered.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 07:52 |
| Last Modified: | 15 Feb 2018 07:52 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/10870 |
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