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UDK 514.116.3                                                

DOI: 10.15507/VMU.025.201501.024

ON THE PROBLEM OF OPTIMIZING OF THE ARRANGEMENT OF SPHERICAL TRIANGLES

Nikonov Vladimir Ivanovich
(associate professor (docent) of Algebra and Geometry chair of Ogarev Mordovia State University (68, Bolshevistskaya Str., Saransk, Russia), Candidate of Sciences (PhD) degree holder in Physico-Mathematical sciences, docent, This email address is being protected from spambots. You need JavaScript enabled to view it.)

Antoshkin Vasiliy Dmitriyevich
( head of Architecture chair of Ogarev Mordovia State University (68, Bolshevistskaya Str., Saransk, Russia), Candidate of Sciences (PhD) degree holder in Engineering sciences, This email address is being protected from spambots. You need JavaScript enabled to view it.)

The paper proposes a solution for the problem of optimizing of location of a triangular network using analytic geometry on a sphere. The authors consider the problem of refinement of equilateral spherical triangle of the smallest area in an equilateral spherical triangle. This problem can be formulated by introducing a polar coordinate system on the sphere and using of some of the results of analytical geometry. The transition from a polar coordinate system to the tangential by introducing the new variables allows to convert the original problem to the solution of a number of simpler problems and to receive an analytical solution. The resulting solution allows for more accurate calculations in optimization problems in the construction of prefabricated spherical shells.

Keywords: spherical segmental shell, triangular net, spherical triangle, spherical distance, area of a spherical triangle. 

For citation: Nikonov V. I., Antoshkin V. D. K zadache optimizatsii raspolozheniya sfericheskikh treugol‌‌nikov [On the problem of optimizing of the arrangement of spherical triangles]. Vestnik Mordovskogo Universiteta – Mordovia University Bulletin. 2015, vol. 25, no. 1, pp. 24–29. DOI: 10.15507/ VMU.025.201501.024 

This work is licensed under a Creative Commons Attribution 4.0 License.