Tight bounds for the dihedral angle sums of a pyramid

Sergey Korotov; Lars Fredrik Lund; Jon Eivind Vatne

Applications of Mathematics (2023)

  • Volume: 68, Issue: 3, page 259-268
  • ISSN: 0862-7940

Abstract

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We prove that eight dihedral angles in a pyramid with an arbitrary quadrilateral base always sum up to a number in the interval ( 3 π , 5 π ) . Moreover, for any number in ( 3 π , 5 π ) 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 π 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.

How to cite

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Korotov, Sergey, Lund, Lars Fredrik, and Vatne, Jon Eivind. "Tight bounds for the dihedral angle sums of a pyramid." Applications of Mathematics 68.3 (2023): 259-268. <http://eudml.org/doc/299514>.

@article{Korotov2023,
abstract = {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.},
author = {Korotov, Sergey, Lund, Lars Fredrik, Vatne, Jon Eivind},
journal = {Applications of Mathematics},
keywords = {pyramid; dihedral angle sum; tight angle bounds},
language = {eng},
number = {3},
pages = {259-268},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Tight bounds for the dihedral angle sums of a pyramid},
url = {http://eudml.org/doc/299514},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Korotov, Sergey
AU - Lund, Lars Fredrik
AU - Vatne, Jon Eivind
TI - Tight bounds for the dihedral angle sums of a pyramid
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 259
EP - 268
AB - 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.
LA - eng
KW - pyramid; dihedral angle sum; tight angle bounds
UR - http://eudml.org/doc/299514
ER -

References

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  8. Khademi, A., Korotov, S., Vatne, J. E., 10.1016/j.cam.2019.03.003, J. Comput. Appl. Math. 358 (2019), 29-33. (2019) Zbl1426.65177MR3926696DOI10.1016/j.cam.2019.03.003
  9. Korotov, S., Vatne, J. E., 10.1016/j.camwa.2019.05.020, Comput. Math. Appl. 80 (2020), 367-370. (2020) Zbl1446.65100MR4099857DOI10.1016/j.camwa.2019.05.020
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