2015/09/07 by Chevallier, Nicolas, Fruchard, Augustin, Vîlcu, Costin
#FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1509.02084
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.