Poncelet problem for rational conics
Author:
V. A. Malyshev
Translated by:
A. Plotkin
Original publication:
Algebra i Analiz, tom 19 (2007), nomer 4.
Journal:
St. Petersburg Math. J. 19 (2008), 597-601
MSC (2000):
Primary 51N20
DOI:
https://doi.org/10.1090/S1061-0022-08-01012-1
Published electronically:
May 9, 2008
MathSciNet review:
2381936
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Abstract | References | Similar Articles | Additional Information
Abstract: The Poncelet problem for rational conics may have a solution only for polygons with $3,4,5,6,7,8,9,10,12,14,16,18,20$, or $24$ vertices.
- Phillip Griffiths and Joseph Harris, On Cayley’s explicit solution to Poncelet’s porism, Enseign. Math. (2) 24 (1978), no. 1-2, 31–40. MR 497281
- V. P. Burskiĭ and A. S. Zhedanov, The Dirichlet problem for the equation of string vibration, the Poncelet problem, the Pell-Abel equation, and some other related problems, Ukraïn. Mat. Zh. 58 (2006), no. 4, 435–450 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 58 (2006), no. 4, 487–504. MR 2272795, DOI https://doi.org/10.1007/s11253-006-0081-x
- V. A. Malyshev, The Abel equation, Algebra i Analiz 13 (2001), no. 6, 1–55 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 13 (2002), no. 6, 893–938. MR 1883839
- V. A. Malyshev, Periods of quadratic irrationalities, and torsion of elliptic curves, Algebra i Analiz 15 (2003), no. 4, 177–203 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 15 (2004), no. 4, 587–602. MR 2068984, DOI https://doi.org/10.1090/S1061-0022-04-00824-6
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Additional Information
V. A. Malyshev
Affiliation:
Rybinsk State Aviation Technology Academy, Rybinsk, Russia
Email:
wmal@ryb.adm.yar.ru
Keywords:
Conics
Received by editor(s):
April 3, 2006
Published electronically:
May 9, 2008
Article copyright:
© Copyright 2008
American Mathematical Society