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An explicit algebro-geometric proof of Poncelet's closure theorem

Buring, R.T. (2013) An explicit algebro-geometric proof of Poncelet's closure theorem. Bachelor's Thesis, Mathematics.

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Poncelet's closure theorem concerns pairs of conics in the plane, and the existence of a fixed point of a certain geometric construction. Griffiths and Harris gave an elegant modern proof of the closure theorem using methods from algebraic geometry, in which an elliptic curve takes the center stage. The proof presented here is similar, but differs in the details. Whereas they used the theory of Riemann surfaces for the details of the proof, a more algebraic and explicit approach is taken here. A connection between the closure theorem and dynamical billiards in ellipses is explored.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:54
Last Modified: 15 Feb 2018 07:54

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