Article
| Title: | Tight bounds for the dihedral angle sums of a pyramid (English) |
| Author: | Korotov, Sergey |
| Author: | Lund, Lars Fredrik |
| Author: | Vatne, Jon Eivind |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 68 |
| Issue: | 3 |
| Year: | 2023 |
| Pages: | 259-268 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We prove that eight dihedral angles in a pyramid with an arbitrary quadrilateral base always sum up to a number in the interval $(3\pi ,5\pi )$. Moreover, for any number in $(3\pi ,5\pi )$ there exists a pyramid whose dihedral angle sum is equal to this number, which means that the lower and upper bounds are tight. Furthermore, the improved (and tight) upper bound $4\pi $ is derived for the class of pyramids with parallelogramic bases. This includes pyramids with rectangular bases, often used in finite element mesh generation and analysis. (English) |
| Keyword: | pyramid |
| Keyword: | dihedral angle sum |
| Keyword: | tight angle bounds |
| MSC: | 51M20 |
| MSC: | 52B10 |
| idZBL: | Zbl 07729496 |
| idMR: | MR4586121 |
| DOI: | 10.21136/AM.2022.0010-22 |
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| Date available: | 2023-05-04T17:35:36Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151653 |
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| Reference: | [8] Khademi, A., Korotov, S., Vatne, J. E.: On the generalization of the Synge-Křížek maximum angle condition for $d$-simplices.J. Comput. Appl. Math. 358 (2019), 29-33. Zbl 1426.65177, MR 3926696, 10.1016/j.cam.2019.03.003 |
| Reference: | [9] Korotov, S., Vatne, J. E.: The minimum angle condition for $d$-simplices.Comput. Math. Appl. 80 (2020), 367-370. Zbl 1446.65100, MR 4099857, 10.1016/j.camwa.2019.05.020 |
| Reference: | [10] Liu, L., Davies, K. B., Yuan, K., Křížek, M.: On symmetric pyramidal finite elements.Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 11 (2004), 213-227. Zbl 1041.65098, MR 2049777 |
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