Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 52A20

Retrieve articles in all journals with MSC (2000): 52A20

Additional Information

Gangsong Leng
Affiliation: Department of Mathematics, Shanghai University, Shanghai, 200436, People’s Republic of China

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