The minimum number of acute dihedral angles of a simplex
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- by Gangsong Leng PDF
- Proc. Amer. Math. Soc. 131 (2003), 3039-3042 Request permission
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
- M. S. Klamkin, L. P. Pook, Acute dihedral angles, Problems 1281, Math. Mag. 61, 5 (1988), 320.
- Rolf Schneider, Convex bodies: the Brunn-Minkowski theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, Cambridge, 1993. MR 1216521, DOI 10.1017/CBO9780511526282
- Lu Yang and Jing Zhong Zhang, A necessary and sufficient condition for embedding a simplex with prescribed dihedral angles in $E^{n}$, Acta Math. Sinica 26 (1983), no. 2, 250–256 (Chinese). MR 694887
Additional Information
- Gangsong Leng
- Affiliation: Department of Mathematics, Shanghai University, Shanghai, 200436, People’s Republic of China
- MR Author ID: 323352
- Email: gleng@mail.shu.edu.cn
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3039-3042
- MSC (2000): Primary 52A20
- DOI: https://doi.org/10.1090/S0002-9939-03-06880-1
- MathSciNet review: 1993210