SOME GEOMETRIC FUNDAMENTALS OF CONSTRUCTION OF CURVED SURFACES IN ARCHITECTURE

Abstract

The article presents the methods of the applied mathematics are presented in the article, namely the applied geometry, that are used in the process of planning of difficult technical forms in engineering and in building at the architectural planning of the difficult crooked surface. In all times architects and designers tried to do the building creations not only technological and strong, and impression vulnerable. On this account architects on this account architects from a deep remoteness began to use the vulnerable geometrical crooked lines. It turned out that most studied and simplest there are the curve lines of the second order in analytical expression. All crooked lines of the second order are the cuts of complete circular conical surface by the planes located under different corners to circular basis of cone. The attractive lines of higher orders can be used in the architectural planning also. Keywords are architecture, planning, the applied geometry, curve of the second order, crooked surface, and surface of the second order. On this account architects and artists from a deep remoteness began to use the geometrical curve lines studies of that and their construction by graphic drawing methods was known yet to the origin of analytical methods in mathematics. It turned out that most studied and simplest there are the crooked lines of the second order in analytical expression. All crooked lines of the second order are the cuts of complete circular conical surface by the planes located under different corners to circular basis of cone. In our time the attractive lines of higher orders can be used in the architectural planning also.