A Question from a Famous Paper of ErdAs
Given a convex body , consider the smallest number so that there is a point such that every circle centred at intersects in at most points. In 1946 ErdAs conjectured that for all , but there are convex bodies for which this is not the case. As far as we know there is no known global upper bound. We show that no convex body has and that there are convex bodies for which .
erdos problem convex curve equidistant points baire category