A postscript on distances in convex \(n\)-gons
Denote by \(g(n)\) the largest \(k\) such that every convex polygon with \(n\) vertices has a vertex \(x\) for which the next \(k\) vertices clockwise from \(x\) or the next \(k\) vertices counterclockwise from \(x\) are successively farther from \(x\). The authors prove that \(g(n) = [n/3] + 1\) for \(n \geq 4\).
scientific article; zbMATH DE number 502911