On the rectification and circle formation problems

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 $\pi$.
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