RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Zap. Nauchn. Sem. POMI: Year: Volume: Issue: Page: Find

 Zap. Nauchn. Sem. POMI, 2009, Volume 372, Pages 97–102 (Mi znsl3561)

On polygons inscribed in a closed space curve

V. V. Makeev

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: Let $n$ be an odd positive integer. It is proved that if $n+2$ is a power of a prime number and $\gamma$ is a regular closed non-self-intersecting curve in $\mathbb R^n$, then $\gamma$ contains vertices of an equilateral $(n+2)$-link polyline with $n+1$ vertices lying in a hyperplane. It is also proved that if $\gamma$ is a rectifiable closed curve in $\mathbb R^n$, then $\gamma$ contains $n+1$ points that lie in a hyperplane and divide $\gamma$ into parts one of which is twice as long as each of the others. Bibl. – 5 titles.

Key words and phrases: Shnirel'man's theorem, equilateral polyline.

Full text: PDF file (156 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2011, 175:5, 556–558

UDC: 514.172

Citation: V. V. Makeev, “On polygons inscribed in a closed space curve”, Geometry and topology. Part 11, Zap. Nauchn. Sem. POMI, 372, POMI, St. Petersburg, 2009, 97–102; J. Math. Sci. (N. Y.), 175:5 (2011), 556–558

Citation in format AMSBIB
\Bibitem{Mak09}
\by V.~V.~Makeev
\paper On polygons inscribed in a~closed space curve
\inbook Geometry and topology. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 372
\pages 97--102
\publ POMI
\mathnet{http://mi.mathnet.ru/znsl3561}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 175
\issue 5
\pages 556--558
\crossref{https://doi.org/10.1007/s10958-011-0367-x}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958064666}