A Question from a Famous Paper of Erdős
نویسندگان
چکیده
Given a convex body K , consider the smallest number N so that there is a point P ∈ ∂K such that every circle centred at P intersects ∂K in at most N points. In 1946 Erdős conjectured that N = 2 for all K , 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 N = ∞ and that there are convex bodies for which N = 6.
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عنوان ژورنال:
- Discrete & Computational Geometry
دوره 50 شماره
صفحات -
تاریخ انتشار 2013