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arXiv · 2001.09525

Minimum area isosceles containers

Gergely Kiss·János Pach·Gábor Somlai
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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 $\sqrt2$ times the area of $T$. Both bounds are best possible.

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Gergely Kiss, János Pach, Gábor Somlai. 2020-01-26. Minimum area isosceles containers. https://arxiv.org/abs/2001.09525

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