Geodesic
On polygons inscribed in a closed space curve
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 97-102
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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. 
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V. V. Makeev. On polygons inscribed in a closed space curve. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 97-102. http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a8/

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