Covering \(n\)-segment unit arcs is not sufficient
In this note the authors construct a compact convex set which contains, for each positive integer \(n\), a congruent copy of any \(n\)-segment polygonal arc of unit length, but not every unit arc. It disproves a conjecture posed by \textit{J. Gerriets} and \textit{G. Poole} in [Am. Math. Mon. 81, 36--41 (1974; Zbl 0279.52007)].
scientific article; zbMATH DE number 5146112