ENGINEERING GEOMETRY AND COMPUTER GRAPHICS

Geometrical models of quadratic-rectangular sets with particular examples of composite solutions

Vestnik MGSU 9/2014
  • Polezhaev Yuriy Olegovich - Moscow State University of Civil Engineering (MGSU) Associate Professor, Department of Descriptive Geometry and Graphics, member of International Union of Russian Artists, Moscow State University of Civil Engineering (MGSU), 6 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-24-83; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Borisova Anzhelika Yur'evna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor Department of Descriptive Geometry and Graphics, Moscow State University of Civil Engineering (MGSU), 6 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-24-83; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Borisova Viktoria Aleksandrovna - Moscow State University of Civil Engineering (MGSU) student, Institute of Environmental Engineering and Mechanization, Moscow State University of Civil Engineering (MGSU), 6 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-24-83; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 161-167

During the current decades the aspect of geometrography compositions formation on the basis of basic images has been actively developed. The basic images possess the qualities of harmonies, expressed by lines, squares, tone, color. The relations of square-rectangular forms belonging to plane geometry of parabolic, hyperbolic and elliptic fields has been already analyzed by scientists. This article introduces equiareals construction of square-rectangular shapes, as well as their rows - in classical composition of elementary figures of "squaring the circle". Variations of such constructions, in their turn, offer the possibility to seek and capture new geometrical graphical compositions, practical application of which can be wide enough in technology design and mechanical engineering, architecture and construction, decoration of household items, arts and crafts and costume fabrics, et cetera. The authors consider the topic of plane geometry "Field-M", which is based on a rectilinear grid of ortholines with circulations in its nodal points. The conclusions made by the authors is that the necessity of solutions for more and more various and complicated problems in the conditions of time limitation determines the development of geometrography methods as an effective operating system along with program methods of cognitive graphics.

DOI: 10.22227/1997-0935.2014.9.161-167

References
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Geometry graphical variationsof the circular conjugate problems

Vestnik MGSU 7/2015
  • Polezhaev Yuriy Olegovich - Moscow State University of Civil Engineering (MGSU) Associate Professor, Department of Descriptive Geometry and Graphics, member, International Union of Russian Artists, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.
  • Borisova Anzhelika Yur’evna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Department of Descriptive Geometry and Graphics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.
  • Borisova Viktoriya Aleksandrovna - Moscow State University of Civil Engineering (MGSU) student, Institute of Environmental Engineering and Mechanization, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Pages 137-146

In civil engineering and architectural design the coupling of circular curves are of great importance. There are different requirements for their practical application, including the possibility of approximation of the curves of higher order. The present article contains a brief excursion into the axiomatic description of the properties and concepts uniting the geometric graphics of a circular, a direct and a point into various compositions. One of the main conjunction theorems is presented, which defines the position and properties of orthoelements of pairing and the sequence of mating arcs using symmetry. The content of the theorem is commented in the form of proof by contradiction, in the form of geometric graphical operations that are naturally consistent with the analytical results. The examples are given of the circular conjunctions closed into oval shapes with a slight difference in the algorithms of composition construction. A particular case of the present configuration is a linear model of squaring the circle, the circle when the medial conjunction coincides with the base circle squaring. Here, the rhomb figure is presented as a basic square and the four successively conjugated circles have their centers at the vertices of squaring, their area are equiareals. Then, the straight “tapered” circular number and variations of its geometry graphical construction are analyzed. The summary results of the considered material are as follows. The main qualitative, quantitative, and typical examples of the circular conjunctions allow competently and variably solving certain problems of geometry graphics in the design process of civil engineering, architecture and applied domestic objects, items and personal things.

DOI: 10.22227/1997-0935.2015.7.137-146

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