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arXiv · 1509.02084

Envelopes of $α$-sections

Nicolas Chevallier·Augustin Fruchard·Costin Vîlcu
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Abstract

Let $K$ be a planar convex body af area $|K|$, and take $0 \textless{} α\textless{} 1$.An $α$-section of $K$ is a line cutting $K$ into two parts, one of whichhas area $α|K|$. This article presents a systematic study of the envelope of $α$-sectionsand its dependence on $α$. Several open questions are asked, one of themin relation to a problem of fair partitioning.

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Nicolas Chevallier, Augustin Fruchard, Costin Vîlcu. 2015-09-07. Envelopes of $α$-sections. https://arxiv.org/abs/1509.02084

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