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The minimum number of acute dihedral angles of a simplex

Author(s): Gangsong Leng
Journal: Proc. Amer. Math. Soc. 131 (2003), 3039-3042.
MSC (2000): Primary 52A20
Posted: May 5, 2003
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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:

1.
M. S. Klamkin, L. P. Pook, Acute dihedral angles, Problems 1281, Math. Mag. 61, 5 (1988), 320.

2.
R. Schneider, Convex Bodies: the Brunn-Minkowski Theory, Cambridge University Press, Cambridge, 1993. MR 94d:52007

3.
L. Yang and J. Z. Zhang, A necessary and sufficient condition for embedding a simplex with prescribed dihedral angles in $E^n ,$ Acta Math. Sinica 26 (1983), 250-256. MR 84g:51023

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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: 10.1090/S0002-9939-03-06880-1
PII: S 0002-9939(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
Posted: May 5, 2003
Additional Notes: This work was supported by the National Natural Sciences Foundation of China (10271071)
Communicated by: Wolfgang Ziller
Copyright of article: Copyright 2003, American Mathematical Society

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