To the Question of the Classification for Analytical Surfaces

Abstract

Until this day, in scientific and technical literature there are descriptions of around 600 analytical surfaces, divided into 38 classes. In turn, it is possible to divide almost each class of surfaces into sub-classes, groups, or types, that is, to compose a classification for surfaces. It will make it easier their further study. For some classes of surfaces there is no sense to set up classification schemes, since these classes consist of a small number of surfaces, or the classification will contain a bare listing of surfaces. These surfaces can include minimal and one-sided surfaces, spiral and helical ones, surfaces of Ciceika and Edlinger, as well as undulating, wavy and corrugated surfaces, and several others. The "others" category includes surfaces which, although highlighted in separate classes, are few, or they are in the process of studying. The study of scientific literature has shown that a classification for revolution surfaces, as well as for transfer and Peterson ones has not yet been set up. This paper is devoted to these classes of analytical surfaces. As the study has showed, it is possible to draw interesting conclusions based on presented classifications. In this paper it has been shown how the appearance of scientific publications devoted to classification for surfaces promote the emergence of numerous works on application of relevant surfaces in architecture, construction, engineering, shipbuilding, light industry products, topography and cartography. But devotion to analytic surfaces’ geometric forms should not be an end in itself in actual practice. So, today architects are passionate about parametric architecture, which is based on knowledge of analytical surfaces’ geometry. However, some leading architects believe that the parametric architecture oversaturated the human life’s space, resulting in a style crisis. Despite architects and engineers’ conflicting opinions, geometers must go ahead of society's immediate demands, creating new forms, classifications, and proposals.