Geodesic
A~Problem of Fejes L.~T\'oth
Matematičeskie trudy, Tome 5 (2002) no. 1, pp. 102-113

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Let $P$ be a convex $n$-gon on the Euclidean plane with edges of lengths $a_1,\dots,a_n$. 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 $\mu(P)=4$. 
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     author = {Yu. G. Nikonorov and N. V. Rasskazova},
     title = {A~Problem of {Fejes} {L.~T\'oth}},
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Yu. G. Nikonorov; N. V. Rasskazova. A~Problem of Fejes L.~T\'oth. Matematičeskie trudy, Tome 5 (2002) no. 1, pp. 102-113. http://geodesic.mathdoc.fr/item/MT_2002_5_1_a6/