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Mat. Tr., 2002, Volume 5, Number 1, Pages 102–113 (Mi mt102)  

This article is cited in 1 scientific paper (total in 1 paper)

A Problem of Fejes L. Tóth

Yu. G. Nikonorov, N. V. Rasskazova

Rubtsovsk Industrial Intitute, Branch of Altai State Technical University

Abstract: Let $P$ be a convex $n$-gon on the Euclidean plane with edges of lengths $a_1,…,a_n$. Denote by $b_i$ the length of the maximal chord of $P$ parallel to $a_i$. For the quantity $\mu(P)=\sum_{i=1}^n{a_i}/{b_i}$, we prove the inequality $3\le\mu(P)\le 4$, which is the Fejes Tóth conjecture. We also give a classification of polygons with $\mu(P)=3$ or $\mu(P)=4$.

Key words: convex body, Euclidean geometry, isoperimetric problem.

Full text: PDF file (6223 kB)
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English version:
Siberian Advances in Mathematics, 2002, 12:4, 34–43

Bibliographic databases:

UDC: 513
Received: 10.09.2001

Citation: Yu. G. Nikonorov, N. V. Rasskazova, “A Problem of Fejes L. Tóth”, Mat. Tr., 5:1 (2002), 102–113; Siberian Adv. Math., 12:4 (2002), 34–43

Citation in format AMSBIB
\Bibitem{NikRas02}
\by Yu.~G.~Nikonorov, N.~V.~Rasskazova
\paper A~Problem of Fejes L.~T\'oth
\jour Mat. Tr.
\yr 2002
\vol 5
\issue 1
\pages 102--113
\mathnet{http://mi.mathnet.ru/mt102}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1918898}
\zmath{https://zbmath.org/?q=an:1049.52009|1015.52005}
\elib{http://elibrary.ru/item.asp?id=9532582}
\transl
\jour Siberian Adv. Math.
\yr 2002
\vol 12
\issue 4
\pages 34--43


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. V. Vasin, Yu. G. Nikonorov, “A Problem of L. Fejes Tóth in a Multidimensional Euclidean Space”, Siberian Adv. Math., 14:2 (2004), 116–125  mathnet  mathscinet  zmath
  • Математические труды Siberian Advances in Mathematics
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