Abstract
Let K be a planar convex body af area |K|, and take 0 < α < 1. An α-section of K is a line cutting K into two parts, one of which has area α|K|. This article presents a systematic study of the envelope of α-sections and its dependence on α. Several open questions are asked, one of them in relation to a problem of fair partitioning.
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APA
Chevallier, N., Fruchard, A., & Vîlcu, C. (2016). Envelopes of α-sections. In Springer Proceedings in Mathematics and Statistics (Vol. 148, pp. 193–218). Springer New York LLC. https://doi.org/10.1007/978-3-319-28186-5_17
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