Helly's Theorems on Convex Domains and Tchebycheff's Approximation Problem

Abstract

Professor Dresden called to our attention the following theorem :If S1, S2, … , Sm are m line segments parallel to the y-axis, all of equal lengths, whose projections on the x-axis are equally spaced, and if we assume that a straight line can be made to intersect every set of three among these segments, then there exists a straight line intersecting all the segments.