Minimum area isosceles containers

Kiss, Gergely and Pach, János and Somlai, Gábor (2020) Minimum area isosceles containers. JOURNAL OF INFORMATION PROCESSING, 28. pp. 759-765. ISSN 0387-5806

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Abstract

We show that every minimum area isosceles triangle containing a given triangle T shares a side and an angle with T. This proves a conjecture of Nandakumar motivated by a computational problem. We use our result to deduce that for every triangle T, (1) there are at most 3 minimum area isosceles triangles that contain T, and (2) there exists an isosceles triangle containing T whose area is smaller than√2 times the area of T. Both bounds are best possible. © 2020 Information Processing Society of Japan.

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