On the problem of optimizing of the arrangement of spherical triangles

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.