Step by step approximation of plane convex bodies (Q1812991)

Let \(K\) be a sufficiently smooth convex body in the plane. \(K\) is approximated by an inscribed or a circumscribed \(n\)-gon which is assigned to a given set \(M_n\) of \(n+1\) real numbers in \([0,1]\). If one number is added to \(M_n\) then one vertex is added to the \(n\)-gon by a deterministic procedure. Using ideas of \textit{D. E. McClure} and \textit{R. A. Vitale} [J. Math. Anal. Appl. 51, 326--358 (1975; Zbl 0315.52004)], the asymptotic behaviour (as \(n\to \infty)\) of the distance of the \(n\)-gon to \(K\) is investigated. In this analysis the concept of dispersion of \(M_n\) (originated in the theory of uniform distribution) plays an essential role.