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

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

- Kapustina O.M., Martynenko Yu.G. Ispol'zovanie sistem simvol'nykh vychisleniy v prepodavanii teoreticheskoy mekhaniki [Application of Symbolic Calculation in Teaching Theoretical Mechanics]. MEI, MGU, Publ., 2012. Available at: http://vuz.exponenta.ru/PDF/book/KapMart2.pdf. Date of access: 21.04.2014.
- Kheyfets A.L. Uchebnyy kurs teoreticheskikh osnov 3D-komp'yuternogo geometricheskogo modelirovaniya i ego perspektivy [Study Course of Theoretical Foundations of 3D Computer Geometric Modeling and its Opportunities]. Informatizatsiya inzhenernogo obrazovaniya : trudy Mezhdunarodnoy nauchno-metodicheskoy konferentsii. INFORINO-2012 (Moskva, 10—11 aprelya 2012 g.) [Information of Engineering Education : Works of International Research and Methodology Conference. INFORINO-2012 (Moscow, April 10—11, 2012)]. Moscow, MEI Publ., 2012, pp. 119—122.
- Kondrat'eva T.M., Polezhaev Yu.O. Chastnye voprosy geometrografii primenitel'no k sisteme "Pole-metr" i kvadrature kruga [Special Questions of Geometrography Relating to the System "Pole-metr" and Quadrature of a Circle]. Inzhenernaya geometrografiya — issledovaniya i razrabotki : sbornik nauchnykh trudov. Moscow, MGSU Publ., 2006.
- Polezhaev Yu.O., Borisova A.Yu., Kondrat'eva T.M. Lineynye puchki v tsirkul'no-ellipticheskikh sootvetstviyakh [Linear Bundles within the Framework of Coincidence of Circle and Ellipse]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 6, pp. 62—67.
- Polezhaev Yu.O., Mitina T.V. Sootnosheniya geometricheskikh elementov kvadratury kruga v «Pole-M» [Correlation of Geometric Entities of the Quadrature of the Circle]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 4, vol. 5, pp. 250—254.
- Arkhimed, Gyugens, Lezhandr, Lambert. O kvadrature kruga [On Squaring the Circle]. Editorial USSR, 2003, 239 p.
- Khal Khellman. Velikie protivostoyaniya v nauke. Desyat' samykh zakhvatyvayushchikh disputov [Great Confrontations in Science. Ten of the Liveliest Disputes Ever]. Moscow, ID Vil'yams Publ., 2007, 320 p.
- Polya G. Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving Combined Edition. 1981, Wiley; Combined edition, 432 p.
- Fedorov E.S. Nachala ucheniya o figurakh [Foundamentals of the Theory of Figures]. Moscow, EE Media Publ., 2012, 418 p.
- Gil'bert D. Osnovaniya geometrii [Foundations of Geometry]. Moscow, Leningrad, OGIZ Publ., 1948, 491 p.
- Hilbert D., Cohn-Vossen S. Anschauliche Geometrie. 1996, Springer; Auflage: 2. Aufl., 365 p.
- Klein F. Neevklidova geometriya [Non-Euclidean Geometry]. Moscow, Leningrad, GTTI Publ., 1936, 355 p.
- Bashlykov A.A. Obraznoe predstavlenie sostoyaniya slozhnykh tekhnologicheskikh ob"ektov upravleniya [Figurative State Representation of Complex Engineering Systems]. Iskusstvennyy intellekt i prinyatie resheniy [Artificial Intellect and Decision-Making]. 2013, no. 3, pp. 9—18. Available at: http://www.aidt.ru/images/documents/2012-03/9_18.pdf. Date of access: 11.09.2013.
- Gornov A.O., Shatsillo L.A. Fraktal'nyy podkhod k strukturirovaniyu geometro-graficheskoy podgotovki [Fractal Approach to Structuring of Geometry-Graphical Education]. Innovatsionnye tekhnologii v inzhenernoy grafike. Problemy i perspektivy : Materialy Mezhdunarodnoy nauchno-prakticheskoy konferentsii (Brest 21 marta 2014 g.) [Innovation Technologies in Engineering Graphics. Problems and Opportuninties : Materials of International Scientific and Practical Conference (Brest, March, 21, 2014)]. Brest, BrGTU Publ., 2014, pp. 19—22. Available at: http://ng.sibstrin.ru/wolchin/img/Brest%202014.pdf. Date of access: 11.05.2014.
- Shcheglov G.A. O kompetentsiyakh CAD/CAE integratsii geometrograficheskikh modeley [On the Competences of CAD/CAE Integration of Geometrographical Models]. Informatsionnye sredstva i tekhnologii : trudy 20 Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii (20—22 noyabrya 2012 g. Moskva) : v 3 t. [Informational Media and Technologies : Works of the 20th International Science and Technical Conference (November 20—22, 2012, Moscow) : in 3 volumes]. Moscow, MEI Publ., 2012, vol. 2, pp. 81—84.