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arXiv · 2108.00326

On the smallest area $n-1$-gon containing a convex $n$-gon

Elliot Hong·Dan Ismailescu·Alex Kwak·Grace Yeeun Park
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Abstract

We prove that every unit area convex pentagon is contained in a convex quadrilateral of area no greater than $3/\sqrt{5}$, and that every unit area convex hexagon is contained in a convex pentagon of area no greater than $7/6$. Both results are tight as the case of the regular pentagon (hexagon) shows. We conjecture that for every $n\ge 6$, every unit area convex $n$ - gon is contained in a $(n-1)$ - gon of area no greater than $1+\tan(2\pi/n)\sec(\pi/n)/n$.

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Elliot Hong, Dan Ismailescu, Alex Kwak, Grace Yeeun Park. 2021-07-31. On the smallest area $n-1$-gon containing a convex $n$-gon. https://arxiv.org/abs/2108.00326

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