Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The minimum number of acute dihedral angles of a simplex


Author: Gangsong Leng
Journal: Proc. Amer. Math. Soc. 131 (2003), 3039-3042
MSC (2000): Primary 52A20
Published electronically: May 5, 2003
MathSciNet review: 1993210
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Abstract | References | Similar Articles | Additional Information

Abstract: For any $n$-dimensional simplex $\Omega\subset R^n$, we confirm a conjecture of Klamkin and Pook (1988) that there are always at least $n$ acute dihedral angles in $\Omega$.


References [Enhancements On Off] (What's this?)

  • 1. M. S. Klamkin, L. P. Pook, Acute dihedral angles, Problems 1281, Math. Mag. 61, 5 (1988), 320.
  • 2. Rolf Schneider, Convex bodies: the Brunn-Minkowski theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, Cambridge, 1993. MR 1216521
  • 3. Lu Yang and Jing Zhong Zhang, A necessary and sufficient condition for embedding a simplex with prescribed dihedral angles in 𝐸ⁿ, Acta Math. Sinica 26 (1983), no. 2, 250–256 (Chinese). MR 694887

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Additional Information

Gangsong Leng
Affiliation: Department of Mathematics, Shanghai University, Shanghai, 200436, People’s Republic of China
Email: gleng@mail.shu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06880-1
Keywords: Simplex, dihedral angle, dual basis
Received by editor(s): May 31, 2000
Received by editor(s) in revised form: August 8, 2001
Published electronically: May 5, 2003
Additional Notes: This work was supported by the National Natural Sciences Foundation of China (10271071)
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2003 American Mathematical Society