Poncelet Theorem

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Karbalaei Harofte, Dorna | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46567 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Jafari, Amir
Abstract:
In this thesis the theorems of Poncelet and Cayley will be discussed. We will use algebraic geometry and in particular the theory of elliptic curves to present a proof following the works of Griffiths and Harris (refrence 1).
The P2-version of poncelet’s theorem that we prove in our thesis says:let C , D be smooth conic in general position. Suppose there is an n-sided olygon inscribed in C and circumscribed about D.Then for any point of C, there exists an n-sided polygen, also inscribed in C and circumscribe about D, which has this point for one of its vertics.the Cayley’s theorem provides a criterion on the existence of such an n-gon given the conics C and D as above
Keywords:
Cone ; Elliptic Curve ; Riemann Surface ; Toris