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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.
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
Linking options:
https://www.mathnet.ru/eng/sm3004https://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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