This article is cited in 3 papers

On One Extremal Problem on the Euclidean Plane

Yu. V. Nikonorova<sup>ab

a</sup> Barnaul State Pedagogical University
^b Rubtsovsk Industrial Intitute, Branch of Altai State Technical University

Abstract: Given two intersecting congruent rectangles $P_1=ABCD$ and $P_2=EFGH$ in the Euclidean plane, let $L_1$ be the length of the part of the boundary $\partial P_1$ which lies in the interior $\operatorname{int}(P_2)$ of $P_2$ and similarly let $L_2$ be the length of the part of $\partial P_2$ which lies in the interior $\operatorname{int}(P_1)$ of $P_1$. The author solves J. W. Fickett's problem of validating the inequality $\frac13 L_1\le L_2\le 3L_1$.

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

UDC: 513

Received: 16.03.2000

 English version: Siberian Advances in Mathematics, 2001, 11:3, 49–59

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