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Poncelet problem for rational conics
Author(s):
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
Posted:
May 9, 2008
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Abstract:
The Poncelet problem for rational conics may have a solution only for polygons with  , or  vertices.
References:
-
- 1.
- P. Griffiths and J. Harris, On Cayley's explicit solution to Poncelet's porism, Enseign. Math. (2) 24 (1978), 31-40. MR 0497281 (80g:51017)
- 2.
- V. P. Burskiĭ and A. S. Zhedanov, The Dirichlet problems for the equation of string vibration, the Poncelet problem, the Pell-Abel equation, and some other related problems, Ukrain. Mat. Zh. 58 (2006), no. 4, 435-450; English transl., Ukrainian Math. J. 58 (2006), no. 4, 487-504. MR 2272795 (2008b:35162)
- 3.
- V. A. Malyshev, The Abel equation, Algebra i Analiz 13 (2001), no. 6, 1-55; English transl., St. Petersburg Math. J. 13 (2002), no. 6, 893-938. MR 1883839 (2003a:14064)
- 4.
- -, Periods of quadratic irrationalities, and torsion of elliptic curves, Algebra i Analiz 15 (2003), no. 4, 177-203; English transl., St. Petersburg Math. J. 15 (2004), no. 4, 587-602. MR 2068984 (2005c:11095)
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Additional Information:
V. A.
Malyshev
Affiliation:
Rybinsk State Aviation Technology Academy, Rybinsk, Russia
Email:
wmal@ryb.adm.yar.ru
DOI:
10.1090/S1061-0022-08-01012-1
PII:
S 1061-0022(08)01012-1
Keywords:
Conics
Received by editor(s):
3/APR/2006
Posted:
May 9, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
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