Geodesic
On the rectification and circle formation problems
Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 177-189

Voir la notice de l'article provenant de la source Math-Net.Ru

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 ($n$) polygon with a nonzero rotation number and with the angle between adjacent sides different from $\pi$. Bibliography: 4 titles. 
@article{SM_1973_19_2_a2,
     author = {Yu. S. Ilyashenko},
     title = {On the rectification and circle formation problems},
     journal = {Sbornik. Mathematics},
     pages = {177--189},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_2_a2/}
}
TY  - JOUR
AU  - Yu. S. Ilyashenko
TI  - On the rectification and circle formation problems
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 177
EP  - 189
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1973_19_2_a2/
LA  - en
ID  - SM_1973_19_2_a2
ER  - 
%0 Journal Article
%A Yu. S. Ilyashenko
%T On the rectification and circle formation problems
%J Sbornik. Mathematics
%D 1973
%P 177-189
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1973_19_2_a2/
%G en
%F SM_1973_19_2_a2
Yu. S. Ilyashenko. On the rectification and circle formation problems. Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 177-189. http://geodesic.mathdoc.fr/item/SM_1973_19_2_a2/