TWO CROFTON FORMULAS IN THE THREE-DIMENSIONAL SPACE

Rafik H. Aramyan; Elen R. Aramyan

doi:10.46991/PYSU:A.2024.58.1.001

TWO CROFTON FORMULAS IN THE THREE-DIMENSIONAL SPACE

Authors

Rafik H. Aramyan Institute of Mathematics of NAS of RA, Armenia; Russian-Armenian University, Armenia https://orcid.org/0000-0003-4003-3088
Elen R. Aramyan Russian-Armenian University, Armenia

DOI:

https://doi.org/10.46991/PYSU:A.2024.58.1.001

Keywords:

integral geometry, convex body, Crofton formula, visual angle

Abstract

In this article, two Crofton-type integral formulas in the three-dimensional Euclidean space are obtained using integral geometry methods.

References

Santalo L. Integral Geometry and Geometric Probability. Cambridge Mathematical Library (2004).

Ambartzumian R.V. Factorization Calculus and Geometrical Probability. Cambridge, Cambridge University Press (1990).

Ambartzumian R.V. Combinatorial Integral Geometry, Metric and Zonoids. Acta Appl. Math. 9 (1987), 3-27. http://dx.doi.org/10.1007/BF00580819

Aramyan R., Mnatsakanyan V. Conditional Moments for a d-Dimensional Convex Body. J. of Contemp. Math. Analysis (Armenian Acad. Sci.) 56 (2021), 3-9. https://doi.org/10.3103/S106836232103002X

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Published

2024-04-23

How to Cite

Aramyan, R. H., & Aramyan, E. R. (2024). TWO CROFTON FORMULAS IN THE THREE-DIMENSIONAL SPACE. Proceedings of the YSU A: Physical and Mathematical Sciences, 58(1 (263), 1–7. https://doi.org/10.46991/PYSU:A.2024.58.1.001