Abstract
Geometers have proposed more than 600 analytical surfaces for implementation. The largest number of these surfaces is used in architecture and mechanical engineering. Although digital architecture and free form architecture are now increasingly influencing the design of long-span shell structures and curved buildings, the research and application of analytical surfaces continues on an increasing scale. The purpose of the research is to study the state of affairs in the application of analytical surfaces in the construction and engineering industries and to clarify the classes of surfaces that have found application in the study of physical phenomena or in solving purely mathematical problems, but not used in other areas of human activity. Another goal is to find analytical surfaces promising for application in architecture and mechanical engineering, which are still little known to architects and engineers. It has been established that, as before, designers take new analytical surfaces to implement their creative ideas from well-studied classes of surfaces of revolution, transfer and umbrella, minimal, ruled, wavy surfaces.
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