Regular Section
Simple Proof of the Lower Bound on the Average Distance from the Fermat-Weber Center of a Convex Body
2022 年 E105.A 巻 5 号 p. 853-857
詳細
2022 年 E105.A 巻 5 号 p. 853-857
We show that for any convex body Q in the plane, the average distance from the Fermat-Weber center of Q to the points in Q is at least Δ(Q)/6, where Δ(Q) denotes the diameter of Q. Our proof is simple and straightforward, since it needs only elementary calculations. This simplifies a previously known proof that is based on Steiner symmetrizations.
