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

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Generalizations of Euler Inequality in the n-dimensional Euclidean Space

  

  1. 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: 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: