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In this paper the issue of approximation of the hyperboloid offset surface off( S ( t ,  v );  d ) at distance  d  by the hyperboloid surface  S  1 ( ϕ ,  v ) is considered. The problem of determining various surfaces approximating the hyperboloid offset surface off ( S ( t ,  v );  d ) is important due to the applications of the hyperboloid as a mathematical model for miscellaneous objects in the architecture and construction industry. The paper presents the method of determining the angles and coordinates of points of various surfaces approximating the hyperboloid of revolution. A two-sheet hyperboloid offset surface can be used for modelling double-layer domes. A one-sheet hyperboloid offset surface was used to model the reinforced structure of the cooling tower.

Hyperboloid offset surface in the architecture and construction industry