A POSTSCRIPT ON DISTANCES IN CONVEX N-GONS

Let g(n) be the largest integer k such that every convex polygon with n vertices and sides has a vertex x such that the next k vertices cloc kwise from x, or the next k vertices counterclockwise from x, are succ essively farther from x. We prove that g(n) = right perpendicular n/3 left perpendicular + 1 for n greater-than-or-equal-to 4. An example gi ves g(n) less-than-or-equal-to right perpendicular n/3 left perpendicu lar + 1, and an extension of a 1952 construction of Leo Moser for a re lated planar problem shows that g(n) greater-than-or-equal-to right pe rpendicular n/3 left perpendicular + 1.