Generalizations of Euler Inequality in the n-dimensional Euclidean Space

Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (2): 218-223.

Generalizations of Euler Inequality in the n-dimensional Euclidean Space

1. Department of Mathematics, Hefei Normal University 2. School of Mathematical Sciences, Anhui University

Received:2010-07-02 Online:2012-06-30 Published:2023-03-29
About author:WANG Wen(1985-), mail, native of Zongyang, Anhui, engages in convex geometry and distance geometry.
Supported by:
Supported by the National Science Foundation of China(60671051)； Supported by the Foundation of Anhui Higher School(KJ2009A45)

Abstract

Abstract: The relation between the circum-radius and the in-radius of an n-dimensional simplex in En is studied. Two new generalizations of Euler inequality for the n-dimensional simplex are established. Besides, we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.

Key words: Euclidean space, simplex, circum-radius, in-radius, altitude, Euler inequality

CLC Number:

O184

WANG Wen, YANG Shi-guo. Generalizations of Euler Inequality in the n-dimensional Euclidean Space[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(2): 218-223.

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Generalizations of Euler Inequality in the n-dimensional Euclidean Space

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