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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.

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

UDC: 514.172
Received: 21.06.2009

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
\publaddr St.~Petersburg
\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}


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