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Mat. Sb. (N.S.), 1973, Volume 90(132), Number 2, Pages 184–195 (Mi msb3004)  

On the rectification and circle formation problems

Yu. S. Ilyashenko


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.

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English version:
Mathematics of the USSR-Sbornik, 1973, 19:2, 177–189

Bibliographic databases:

UDC: 513.7
MSC: Primary 92A05; Secondary 34C35
Received: 10.05.1972

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/msb3004}
\mathscinet{http://www.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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