Authors: Dragović, Vladimir 
Radnović, Milena
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Introduction to poncelet porisms
Journal: Poncelet Porisms and Beyond
Series/Report no.: Frontiers in Mathematics
Volume: 2011
First page: 1
Last page: 300
Issue Date: 23-May-2011
ISBN: 978-3-034-80014-3
ISSN: 1660-8046
DOI: 10.1007/978-3-0348-0015-0_1
“One of the most important and also most beautiful theorems in classical geometry is that of Poncelet (…) His proof was synthetic and somewhat elaborate in what was to become the predominant style in projective geometry of last century. Slightly thereafter, Jacobi gave another argument based on the addition theorem for elliptic functions. In fact, as will be seen below, the Poncelet theorem and addition theorem are essentially equivalent, so that at least in principle Poncelet gave a synthetic derivation of the group law on an elliptic curve. Because of the appeal of the appeal of the Poncelet theorem it seems reasonable to look for higher-dimensional analogues… Although this has not yet turned out to be the case in the Poncelet-type problems…”
Keywords: Elliptic Curve | Addition Theorem | Baxter Equation | Billiard Trajectory | Billiard System
Publisher: Springer Link

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