page 3 (English version) _____ ARCHITECTURE AND MATHEMATICS
MAIN ENGLISH PAGE RUSSIAN VERSION (Syr for Windows) About the course STUDENTS' WORKS PROGRAM GUEST'S BOOK Literature (in Russian)
S u m m a r y
______The article about the relation to each other of two disciplines architecture and mathematics, about their influence against each other, about comparison of these disciplines and about an opportunity of the analysis of each of them by methods another. The construction of each mathematical unit begins with creation of some list, so-called, "not determined" concepts (objects) and rules (axioms and postulates), on which these objects are included among themselves into the certain relations. Thus from these primary elements, in turn, further the new objects and designs can be formed which are elements of the uniform general system carrying brightly expressed hierarchical structure. If at construction of the above stated mathematical design all rules of mathematics were observed, this structure gets logic stability, composite integrity and completeness.
______If to summarise told on language of architecture, it is possible to tell, that the mathe-matics is a grandiose mental, ideal structure, which in curtailed, conceptual, symbolical, kind simulates the world, environmental us, and phenomena, occurring in it. "Base" of this structure is formed by not determined concepts, and "tectonic" is defined by those by logic communications, which are entered between these fundamental concepts. All structure is beautiful, is harmonious and it is aesthetically expedient, both as a whole, and in any part. And, though on each moment of construction it has that we name by completeness and integrity, in view of inexhaustible of the world, environmental us, nei-ther in large, nor in small, its erection always can be continued, not breaking harmony neither in general, nor in private.
______Architecture, as well as the mathematics, deals with the certain structures having strictly hierarchical character. The analogue of not determined concepts in mathematics, for the architecture is served by quite real objects: the bricks, elements of modular rein-forced-concrete etc. From them are under construction apartment houses, room blocks, the inhabited and industrial cases are erected. In turn, these objects are components of objects more high levels: ensembles, quarters, industrial complexes and etc. Following level of architectural creativity settlements, industrial zones, cities, areas and whole regions. And, at each level all architectural objects and their associations, except for their functional im-portance, should have integrity, composite completeness and, that for architecture is not less important, to be beautiful, that is to have aesthetic value.
______Thus, in architecture also, as well as in mathematics, the multilevel hierarchical structure is precisely traced. As well as in mathematics, each level, its each component, are subordinated to internal logic and general plan, have beauty, and completeness.

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