RULED BUT NOT FLAT SURFACES IN SCIENCE, TECHNOLOGY AND ARCHITECTURAL BUILDINGS

This work is devoted to the analysis of features of linear surfaces of rotation and their application in various areas of human activity. The article carries out a geometric and practical study of the surfaces of a cone, a cylinder, and a single-cavity hyperboloid as representatives of linear surfaces of rotation. Their mathematical description is presented and geometric models are developed: visual image schemes in a rectangular coordinate system and two-picture complex drawings are created. Special attention is paid to the practical application of these surfaces in various fields, in particular in the fields of mechanical engineering and architecture. Due to its geometric shape, the conical surface of rotation is used when connecting parts, at the ends of shafts, in water fittings, etc. Objects of everyday life have the surface of a truncated cone: vases for flowers, buckets, funnels for pouring liquids, a lamp with a lampshade in the form of a cone, etc. In architecture, the conical surface has been used since ancient times as a roof for residential premises and ancient castles, for chimneys, lighthouse towers, etc. In Muslim cities, a cylindrical surface of rotation is used for the construction of minarets, which ends at the top with a conical roof, symbolizing the desire for heaven. The cylindrical surface was used for the construction of towers of ancient fortresses and modern buildings of various purposes. Products having the shape of a cylinder of rotation are widely used in engineering and military industry, medicine, computer graphics, etc. Numerous cooling towers, high-rise towers, etc., have the geometric shape of a single-cavity hyperboloid. In the article, the most characteristic vivid examples of the use of the surfaces of a cone, cylinder, and single-cavity hyperboloid are selected, their features are analyzed, and photographic images are presented.