Geodesic
On the rectification and circle formation problems
Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 177-189 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The rectification and circle formation problems were posed by A. M. Leontovich, I. I. Pyatetskii-Shapiro and O. N. Stavskaya (Automat. i Telemeh. No 4, 1970; No 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},
     year = {1973},
     volume = {19},
     number = {2},
     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
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
%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/

[1] A. M. Leontovich, I. I. Pyatetskii-Shapiro, O. N. Stavskaya, “Zadacha okruzhivaniya v matematicheskoi modeli formoobrazovaniya”, Avtomatika i telemekhanika, no. 2, 1971, 100–110 | MR | Zbl

[2] A. M. Leontovich, I. I. Pyatetskii-Shapiro, O. N. Stavskaya, “Nekotorye matematicheskie zadachi, svyazannye s formoobrazovaniem”, Avtomatika i telemekhanika, no. 4, 1970, 94–107 | MR | Zbl

[3] A. M. Leontovich, “Skorost skhodimosti v zadache okruzhivaniya”, Matem. sb., 88 (130) (1972), 88–117 | Zbl

[4] O. N. Stavskaya, “Issledovanie skhodimosti v zadache spryamleniya”, Matem. sb., 88 (130) (1972), 118–136