ENGINEERING GEOMETRY AND COMPUTER GRAPHICS

Geometry graphical variationsof the circular conjugate problems

Вестник МГСУ 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.

Страницы 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

Библиографический список
  1. Volynskov V.E. Prostranstvennoe formoobrazovanie i ego arkhetipy [Space Forming and its Archetypes]. Vestnik Volgogradskogo gosudarstvennogo arkhitekturno-stoitel’nogo universiteta [Proceedings of Volgograd State University of Architecture and Civil Engineering. 2009, no. 13, pp. 124—129. (In Russian)
  2. Krylova O.V., Polezhaev Yu.O., Tel'noy V.I. Deduktivnyy aspekt postroeniya izometricheskikh monoproektsiy [Deductive Aspect of Isometric Monoprojections Creation]. Fundamental'nye nauki v sovremennom stroitel'stve: Sbornik dokladov Shestoy nauchno-prakticheskoy i uchebno-metodicheskoy konferentsii [Fundamental Sciences in the Modern Construction]. Moscow, MGSU Publ., 2008, pp. 163—165. (In Russian)
  3. Pólya G. Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving, 2 volumes, Wiley 1962.
  4. Gilbert de B. Robinson. The Foundations of Geometry. U. of Toronto; Fourth edition, 1946.
  5. 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. (In Russian)
  6. Stepura E.A., Zontov R.A. Provedenie pryamoy cherez nedostupnuyu tochku [Drawing a straight through a Remote Point]. Sbornik trudov 2-y Vserossiyskoy nauchno-metodicheskoy konferentsii po inzhenernoy geometrii i komp'yuternoy grafike [Collection of Works of the 2nd All-Russian Scientific Conference on Engineering Geometry and Computer Graphics]. Moscow, MITKhT Publ., 2009, pp. 103—110. (In Russian)
  7. Polezhaev Yu.O., Borisova A.Yu. Lineynye variatsii modelirovaniya svoystv elliptichnosti [Modeling the Properties of Ellipticity: Linear Variations]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 8, pp. 34—38. (In Russian)
  8. Kon-Fossen S. Gilbert D. Naglyadnaya geometriya [Visual Geometry]. 5th edition, Moscow, Editorial USSR, 2010, 344 p. (In Russian)
  9. Klein F. Neevklidovaya geometriya [Non-Euclidean geometry]. Transl. from German. Moscow, Leningrad, GGTI, 1936, 358 p. (In Russian)
  10. Semple J.G., Kneebone G.T. Algebraic Projective Geometry. Oxford, Oxford University Press, 1952, 405 p.
  11. Coxeter H.S.M. Projective Geometry. New York, Blaisdell Publishing Co, 1964, 162 p.
  12. Fedorov E.S. Nachala ucheniya o figurakh [Bases of the Theory of Figures]. Moscow, EE Media Publ., 2012, 418 p. (In Russian)
  13. Lelon-Ferran Zh. Osnovaniya geometrii [Fundamentals of Geometry]. Transl. from France. Moscow, Mir Publ., 1989, 312 p. (In Russian)
  14. Polezhaev Yu.O., Mitina T.V. K voprosu o metodike resheniya zadach intsidentsii [On the Methodology of Solving Incidence Problems]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2007, no. 1, p. 81. (In Russian)
  15. Vol'berg O.A. Osnovnye idei proektivnoy geometrii [Basic Ideas of Projective Geometry]. 4th edition. Moscow, Editorial URSS Publ., 2009, 192 p. (Nauku vsem — Shedevry nauchno-populyarnoy literatury [Science to Everyone — Masterpieces of Popular Scientific Literature]) (In Russian)
  16. Odesskiy P.D. O teoriyakh prochnosti i effekte vtoroy nagruzki primenitel'no k stal'nym stroitel'nym konstruktsiyam [On Strength Theories of the Effect of the Second Load Applied to the Steel Building Structures]. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering]. 2013, no. 10, pp. 20—24. (In Russian)
  17. Zhilkina T.A. Rol' prostranstvennogo myshleniya v praktike prepodavaniya graficheskikh distsiplin v tekhnicheskikh vuzakh [The Role of Spatial Thinking in the Practice of Teaching Graphic Disciplines in Technical Universities]. Nauka i obrazovanie: problemy i tendentsii : materialy Mezhdunarodnoy nauchno-prakticheskoy konferentsii [Science and Education: Problems and Tendencies : Materials of the International Science and Practice Conference]. Ufa, December 20—21 2013 : in three parts. Ufa, RITs BashGU Publ., 2013, part 2, pp. 142—146. (In Russian)
  18. Znamenskaya E.P., Ruzaev A.M. Geometricheskaya interpretatsiya rezul'tatov poiska optimal'nykh resheniy stroitel'nykh konstruktsiy [Geometric Interpretation of Search for Optimal Solutions for Building Structures]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 4, vol. 1, pp. 113—116. (In Russian)
  19. Polezhaev Yu.O., Fatkullina A.A., Borisova A.Yu. Geometricheskie modeli sopryazheniy kvadrik na fragmentakh arkhitekturnykh ob”ektov [Geometric Models of Junctions of Quadrics in Fragments of Architectural Pieces]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 9, pp. 18—23. (In Russian)
  20. Martynyuk A.N., Matveev O.A., Ptitsyna I.V. Elementy proektivnoy geometrii [Projective Geometry Elements]. Moscow, MGOU Publ., 2010, 134 p. (In Russian)
  21. Zacharias M. Vvedenie v proektivnuyu geometriyu [Introduction into Projective Geometry]. Transl. from German. Moscow, LIBROKOM Publ., 2010, 90 p. (Fiziko-matematicheskoe nasledie: matematika (geometriya) [Physical and Mathematical Heritage: Mathematics (Geometry)]. (In Russian)
  22. Polezhaev Yu.O., Donskaya O.V. Osobennosti vzaimosvyazey inzhenerno-tekhnicheskogo i khudozhestvennogo risunka. K voprosu o vozrozhdenii akademicheskikh traditsiy [Interaction Features of Engineering Technical and Artistic Drawing. To the Question of Academical Tradition Revival]. Dekorativnoe iskusstvo i predmetno-prostranstvennaya sreda. Vestnik MGKhPA [Decorative Art and Environment. Gerald of the Moscow State Academy of Applied Art and Design named after Sergei Stroganov]. 2012, no. 2-2, pp. 247—252. (In Russian)
  23. Georgievskiy O.V. Khudozhestvenno-graficheskoe oformlenie arkhitekturno-stroitel'nykh chertezhey [Art and Graphic Design of Architectural Drawings]. Moscow, Arkhitektura-S Publ., 2004, 79 p. (In Russian)
  24. Gusakova I.M. Rol' tonal'nogo risunka na poiskovom etape raboty nad dekorativnoy kompozitsiey po distsipline «Materialovedenie, tekhnologiya i proizvodstvennoe obuchenie» [The Role of the Tonal Drawing on the Exploratory Phase of the Decorative Composition on the Subject “Materials Science, Technology and Vocational Training”]. Prepodavatel' XXI vek [A teacher of the 21st Century]. 2014, no. 1, part 1, pp. 170—175. (In Russian)

Скачать статью

Результаты 1 - 1 из 1