Abstract
Abstract 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.
Highlights
A twosheet hyperboloid offset surface can be used for modelling double-layer domes
A one-sheet hyperboloid is often used as a model for various objects in the construction industry
We provide a convenient method for determining the angles and coordinates of points of various surfaces approximating the twosheet hyperboloid surface
Summary
A one-sheet hyperboloid is often used as a model for various objects in the construction industry One-sheet hyperboloid shaped constructions can be built with, for example straight steel elements that form a strong structure. Such a clever design guarantees lower costs than other technical solutions. To design structures based on the hyperboloid S(t, v), the coordinates of points of other surfaces that approximate the hyperboloid S(t, v) are necessary.
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