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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Poncelet's theorem in space


Author: Emma Previato
Journal: Proc. Amer. Math. Soc. 127 (1999), 2547-2556
MSC (1991): Primary 14H40; Secondary 58F07
Published electronically: May 4, 1999
MathSciNet review: 1662198
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Abstract: A plane polygon $\mathcal{P}$ inscribed in a conic $C$ and circumscribed to a conic $D$ can be continuously `rotated', as it were. One of the many proofs consists in viewing each side of $\mathcal{P}$ as translation by a torsion point of an elliptic curve. In the $n$-space version, involving torsion points of hyperelliptic Jacobians, there is a $g=(n-1)$-dimensional family of rotations, where $g=\text{genus}$ of the hyperelliptic curve; the polygon is now inscribed in one and circumscribed to $n-1$ quadrics.


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Additional Information

Emma Previato
Affiliation: Department of Mathematics, Boston University, Boston, Massachusetts 02215
Email: ep@math.bu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05307-1
PII: S 0002-9939(99)05307-1
Received by editor(s): May 20, 1997
Received by editor(s) in revised form: September 28, 1997
Published electronically: May 4, 1999
Additional Notes: The author’s research was partly supported by NSA grant MDA904-95-H-1031
Communicated by: Ron Donagi
Article copyright: © Copyright 1999 American Mathematical Society