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Mathematics of the USSR-Sbornik, 1973, Volume 19, Issue 2, Pages 177–189
DOI: https://doi.org/10.1070/SM1973v019n02ABEH001744
(Mi sm3004)
 

On the rectification and circle formation problems

Yu. S. Ilyashenko
References:
Abstract: The rectification and circle formation problems were posed by A. M. Leontovich, I. I. Pyatetskii-Shapiro and O. N. Stavskaya (Automat. i Telemeh. № 4, 1970; № 2, 1971). In this paper we set up a rule which achieves the rectification of an arbitrary “admissible” nonclosed polygonal line (i.e. a polygonal line in which no section degenerates to a point nor lies on the preceding or following section). For each natural number $N$ we prove the existence of a similar rule which effects circle formation of an arbitrary $n$-sided ($n<N$) polygon with a nonzero rotation number and with the angle between adjacent sides different from $\pi$.
Bibliography: 4 titles.
Received: 10.05.1972
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1973, Volume 90(132), Number 2, Pages 184–195
Bibliographic databases:
Document Type: Article
UDC: 513.7
MSC: Primary 92A05; Secondary 34C35
Language: English
Original paper language: Russian
Citation: Yu. S. Ilyashenko, “On the rectification and circle formation problems”, Mat. Sb. (N.S.), 90(132):2 (1973), 184–195; Math. USSR-Sb., 19:2 (1973), 177–189
Citation in format AMSBIB
\Bibitem{Ily73}
\by Yu.~S.~Ilyashenko
\paper On the rectification and circle formation problems
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 90(132)
\issue 2
\pages 184--195
\mathnet{http://mi.mathnet.ru/sm3004}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=334288}
\zmath{https://zbmath.org/?q=an:0261.34030}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 2
\pages 177--189
\crossref{https://doi.org/10.1070/SM1973v019n02ABEH001744}
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  • https://doi.org/10.1070/SM1973v019n02ABEH001744
  • https://www.mathnet.ru/eng/sm/v132/i2/p184
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    Abstract page:345
    Russian version PDF:123
    English version PDF:10
    References:51
    First page:2
     
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