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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 $a_1,\dots,a_n$. 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 $\mu(P)=4$.
Key words:
convex body, Euclidean geometry, isoperimetric problem.
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
Linking options:
https://www.mathnet.ru/eng/mt102 https://www.mathnet.ru/eng/mt/v5/i1/p102
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