Maria Calvo and Vicente Munoz, The most inaccessible point of a convex domain,
Forum Geometricorum, 13 (2013) 37--52.
Abstract. The inaccessibility of a point p in a bounded domain D subset
R^n is the minimum of the lengths of segments through p with
boundary at bd D. The points of maximum inaccessibility I_D are
those where the inaccessibility achieves its maximum. We prove that
for strictly convex domains, I_D is either a point or a segment,
and that for a planar polygon I_D is in general a point. We study
the case of a triangle, showing that this point is not any of the
classical notable points.
[ps file]
[pdf]