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Simple Proof of the Lower Bound on the Average Distance from the Fermat-Weber Center of a Convex Body
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Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.5 pp.853-857
- Publication Date
- 2022/05/01
- Publicized
- 2021/11/15
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021EAP1103
- Type of Manuscript
- PAPER
- Category
- Numerical Analysis and Optimization
Authors
Xuehou TAN
Tokai University
Keyword
Latest Issue
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Xuehou TAN, "Simple Proof of the Lower Bound on the Average Distance from the Fermat-Weber Center of a Convex Body" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 5, pp. 853-857, May 2022, doi: 10.1587/transfun.2021EAP1103.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1103/_p
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@ARTICLE{e105-a_5_853,
author={Xuehou TAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Simple Proof of the Lower Bound on the Average Distance from the Fermat-Weber Center of a Convex Body},
year={2022},
volume={E105-A},
number={5},
pages={853-857},
abstract={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.},
keywords={},
doi={10.1587/transfun.2021EAP1103},
ISSN={1745-1337},
month={May},}
Copy
TY - JOUR
TI - Simple Proof of the Lower Bound on the Average Distance from the Fermat-Weber Center of a Convex Body
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 853
EP - 857
AU - Xuehou TAN
PY - 2022
DO - 10.1587/transfun.2021EAP1103
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2022
AB - 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.
ER -
English
