Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2012, Number 3, Pages 43–47 (Mi vmumm496)  
This article is cited in 2 scientific papers (total in 2 papers)

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Metric properties of poncelet polygonal lines

E. A. Avksentyev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (323 kB) Citations (2)
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Abstract: A generalization of the Radić-Kaliman theorem on metric relations in Poncelet polygonal curves is obtained in the papaer. A general principle for determination of condition for a closure of a Poncelet polygonal curve for two circles is derived from this result. In particular, explicit formulas for the inscribed-circumscribed $n$-gon for $n=5,6,8$ and an algorithm for finding such formulas for all $n$ are obtained.
Key words: Poncelet theorem, inscribed-circumscribed $n$-gon, pencil of circles, closure theorems, closure conditions.
Received: 07.06.2010
English version:
Moscow University Mathematics Bulletin, 2012, Volume 67, Issue 3, Pages 116–120
DOI: https://doi.org/10.3103/S0027132212030060
Bibliographic databases:
Document Type: Article
UDC: 514
Language: Russian
Citation: E. A. Avksentyev, “Metric properties of poncelet polygonal lines”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 3, 43–47; Moscow University Mathematics Bulletin, 67:3 (2012), 116–120
Citation in format AMSBIB
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\by E.~A.~Avksentyev
\paper Metric properties of poncelet polygonal lines
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2012
\issue 3
\pages 43--47
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3026842}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2012
\vol 67
\issue 3
\pages 116--120
\crossref{https://doi.org/10.3103/S0027132212030060}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864810931}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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