The radial mean bodies of triangles in the plane

YIN Leiqin1; CHEN Yanni2*

doi:10.15983/j.cnki.jsnu.2023110

Journal of Shaanxi Normal University(Natural Science Edition) >

2023 , Vol. 51 >Issue 1: 60 - 65

DOI: https://doi.org/10.15983/j.cnki.jsnu.2023110

The radial mean bodies of triangles in the plane

YIN Leiqin1 ,
CHEN Yanni2*

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(1 School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;2 School of Mathematics and Statistics，Shaanxi Normal University，Xian 710119，Shaanxi，China)

Online published: 2023-05-06

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Abstract

The radial mean bodies of triangles in the plane are discussed and found that they are hexagons with symmetric origin. An example can be provided to prove the radial mean bodies have not the monotonicity. Then, the relation of inclusion between radial mean bodies and John ellipsoid are obtained.

Key words： radial mean body; John ellipsoid; X-ray symmetrization

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YIN Leiqin1 , CHEN Yanni2* . The radial mean bodies of triangles in the plane[J]. Journal of Shaanxi Normal University(Natural Science Edition), 2023 , 51(1) : 60 -65 . DOI: 10.15983/j.cnki.jsnu.2023110

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