An Identity and Its Applications Concerning Two Mass-points Systems

doi:10.13371/j.cnki.chin.q.j.m.2015.03.007

Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (3): 366-372.doi: 10.13371/j.cnki.chin.q.j.m.2015.03.007

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An Identity and Its Applications Concerning Two Mass-points Systems

The Yuanling No.1 Midlde School

Received:2013-05-26 Online:2015-09-30 Published:2020-11-20
About author:ZHOU Yong-guo(1962-), male, native of Yuanling, Hunan, a senior teacher in Yuanling No.1 Middle School, engages in elementary mathematics and high-dimensional convex bodies geometry.

Abstract

Abstract: In this paper, we first give and prove a geometric identity for distance between any point and mass-points of two mass-points systems in n-dimensional Euclidean space Rn.As its application, we obtain an equality for two mass-points systems and its radius of the circumscribed sphere and an inequality for distance between mass-points of two mass-points systems and its k-dimensional volume.

Key words: mass-points system, distance, volume, geometric identity, geometric inequality

CLC Number:

O178

ZHOU Yong-guo. An Identity and Its Applications Concerning Two Mass-points Systems[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(3): 366-372.

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An Identity and Its Applications Concerning Two Mass-points Systems

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