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    Academic Journal

    Συγγραφείς: Kosobutskyy, P., Karkulovska, M., Morgulis, A.

    Συνεισφορές: The City University of New York

    Θέμα γεωγραφικό: Львів, Lviv

    Time: 621, 510, 004, 519

    Περιγραφή αρχείου: 75-89; application/pdf; image/png

    Relation: Вісник Національного університету “Львівська політехніка”. Серія: Комп’ютерні системи проектування теорія і практика, 908, 2018; http://arxiv.org/abs/physics/0509207; https://arxiv.org/ftp/arxiv/papers/1801/1801.01369.pdf; http://www4.ncsu.edu/~njrose/pdfFiles/GoldenMean.pdf; https://artmatlab.ru/templates/text/r_display/editor/ac49/or01.pdf; 1. Shene P., Kosnar M., Gardian I. et. al. Mathematics and CAD. In two books. Book 1. Basic methods of the theory of poles. Moscow: Myr, 1988.; 2. Zharmen-Lakur P., Georges P., Pistre F., Bezier P. Mathematics and CAD. In two books. Book 2. Basic methods of the theory of poles. Moscow: Myr, 1989.; 3. Pacioli di Borgo L. De Divina Proportione. On Divine Proportion. 1509.; 4. Zeising A. Neue Lehre von den Proportionen des menschlischen Körpers. New Theory of the Proportions of Human Bodies. Leipzig: Weigel, 1854.; 5. Zeising A. Äesthetische Forschungen. Aesthetic Research. Frankfurt: Medinger, 1855.; 6. Fechner G. Über die frage des golden Schnitts. On the question of the golden section. Arch Zeich Künste, 1865.; 7. Vorobyov N.N., Fibonacci Numbers. Moscow: Nauka, 1961.; 8. V.Hoggat V. Fibonacci and Lucas Numbers. MA: Houghton Mifflin, Boston, 1969.; 9. Shechtman D. Crystals of golden proportions. Ann Fernholm, The Nobel Prize in Chemistry 2011, The Swedish Academy of Sciences.; 11. Grushina N. V., Korolenko P. V., Perestoronin P. A. Fractal structures and “Golden” ratio in optics // Preprint of the Physics Faculty of M. V. Lomonosov Moscow State University 2007, 6: 58.; 12. Heyrovska, S. Narayan, et. al. Doi:arXiv:physics/0509207; http://arxiv.org/abs/physics/0509207; 13. Daqiu Yu, Dongfeng Xue, and Henryk Ratajczak. Golden ratio and bond-valence parameters of hydrogen bonds of hydrated borates // Journal of Molecular Structure 2006, 783: 210–214.; 14. Sherbon M. Fine-Structure Constant from Golden Ratio Geometry // International Journal of Physical Research 2017, 2 (1): 89.; 15. Affleck I. Solid-state physics: golden ratio seen in a magnet // Nature 2010, 464 (7287): 362–363.; 16. Semenyuta N.F. On the relationship of parameters of chain circuits with recurrent numerical sequences // Theoretical electrical engineering, Lviv: High school 1974, 17: 23–25.; 17. Semenuta N.F. Analysis of electrical circuits by the recurrence number method // Electric communication on railway transport. Proceedings of the Belarusian Institute of Railway Transport Engineers. Gomel: Bel.IRTE, 1974, 134: 3–19.; 18. Gazale Midhat J. Gnomon. From Pharaohs to Fractals. Princeton, New Jersey: Princeton University Press, 1999.; 19. Omotehinwa T. O., Ramon S. O. // International Journal of Computer and Information Technology 2013, 02(04): 630.; 20. Pletser V., https://arxiv.org/ftp/arxiv/papers/1801/1801.01369.pdf.; 21. Nicholas J. Rose. The Golden Mean and Fibonacci Numbers. From Web Resource: http://www4.ncsu.edu/~njrose/pdfFiles/GoldenMean.pdf.; 22. Philip J. Davis. Spirals from Theodorus to Chaos. A. K. Peterss, Wellesley, MA., 1993.; 23. Matthew Oster. A spiral of triangles related to the great pyramid // The Mathematical Spectrum 2005-06, 38: 108–112.; 24. Prodinger H. The asymptotic behavior of the golden numbers // Fibonacci Quarterly 1996, 34.3: 224–225; fq.math.ca/Scanned/34-3/prodinger.pdf.; 25. V. de Spinadel. On characterization of the onset to chaos // Chaos, Solitons and Fractals 1997, 8 (10): 1631–1643.; 26. V. de Spinadel. The metallic means family and multifractal spectra // Nonlinear Analysis 1999, 36: 721–745.; 27. Bradley S. A geometric connection between generalized Fibonacci sequences and nearly golden sections // Fibonacci Quarterly 2000, 38.2: 174–179. –fq.math.ca/Scanned/38-2/bradley.pdf.; 28. Stakhov А. Generalized Golden Sections and a new approach to the geometric definition of a number // Ukrainian Mathematical Journal 2004, 56 (8): 1143–1150.; 29. Stakhov А. The Generalized Principle of the Golden Section and its Applications in Mathematics, Science and Engineering // Chaos, Solitons & Fractals 2005, 26(2): 263–289.; 30. Stakhov А. Fundamentals of a new kind of Mathematics based on the Golden Section // Chaos, Solitons & Fractals 2005, 27(5): 1124–1146.; 31. V. de Spinadel. The Metallic means Family and Art Aplimat // Journal of Appl. Mathematics 2010, 3(1): 53–64.; 32. Vasilenko S. Generalized recursions with attractor of the golden section. From Web Resource: https://artmatlab.ru/templates/text/r_display/editor/ac49/or01.pdf.; 33. Huntley H. The Divine Proportion: A Study in Mathematical Beauty. Dover Publications, Inc., New York, 1970.; 34. Vajda S. Fibonacci & Lucas Numbers, and the Golden Section. Theory and Applications. Ellis Horwood limited, 1989.; 35. Dunlap R. The golden ratio and Fibonacci numbers. World Scientific Publishing Co. Pte. Ltd. 1997.; 36. Stakhov A. The Golden Section and Modern Harmony Mathmatics // Applications of Fibonacci numbers, Vol. 7 (Graz, 1996), Kluwer Academic Publishers, 1998, pp. 393–399.; 37. Kappraff J. Connections. The geometric bridge between Art and Science. Second Edition. Singapore, New Jersey, London. World Scientific, 2001: 490.; 38. Kappraff J. Beyond Measure A Guided Tour Through Nature, Myth and Number. Singapore, New Jersey, London, Hong Kong. World Scientific, 2002: 584.; 39. Koshy Т. Fibonacci and Lucas numbers with application. A Wiley-Interscience Publication: New York, 2001.; 40. Bodnar О. The Golden Section and Non-Euclidean Geometry in Science and Art. Lviv: Publishing House “Ukrainian Technologies”, 2005 (Ukrainian).; 41. P.Kosobutskyy. On the Possibility of Constructinga Set of Numbers with Golden Section Properties. International Conference: Algebra and Analysis with Application. July 1-4 2018, Ohrid, Republic of Macedonia.; 42. Schneider R. A Golden Product Identity for e // Mathematics Magazine 2014, 87(2): 132–134.; 43. Shneider R. Fibonacci numbers and the golden ratio. VarXiv: 1611.07384v1 [math.HO] 22 Nov 2016.; 11. Grushina N. V., Korolenko P. V., Perestoronin P. A. Fractal structures and "Golden" ratio in optics, Preprint of the Physics Faculty of M. V. Lomonosov Moscow State University 2007, 6: 58.; 13. Daqiu Yu, Dongfeng Xue, and Henryk Ratajczak. Golden ratio and bond-valence parameters of hydrogen bonds of hydrated borates, Journal of Molecular Structure 2006, 783: 210–214.; 14. Sherbon M. Fine-Structure Constant from Golden Ratio Geometry, International Journal of Physical Research 2017, 2 (1): 89.; 15. Affleck I. Solid-state physics: golden ratio seen in a magnet, Nature 2010, 464 (7287): 362–363.; 16. Semenyuta N.F. On the relationship of parameters of chain circuits with recurrent numerical sequences, Theoretical electrical engineering, Lviv: High school 1974, 17: 23–25.; 17. Semenuta N.F. Analysis of electrical circuits by the recurrence number method, Electric communication on railway transport. Proceedings of the Belarusian Institute of Railway Transport Engineers. Gomel: Bel.IRTE, 1974, 134: 3–19.; 19. Omotehinwa T. O., Ramon S. O., International Journal of Computer and Information Technology 2013, 02(04): 630.; 23. Matthew Oster. A spiral of triangles related to the great pyramid, The Mathematical Spectrum 2005-06, 38: 108–112.; 24. Prodinger H. The asymptotic behavior of the golden numbers, Fibonacci Quarterly 1996, 34.3: 224–225; fq.math.ca/Scanned/34-3/prodinger.pdf.; 25. V. de Spinadel. On characterization of the onset to chaos, Chaos, Solitons and Fractals 1997, 8 (10): 1631–1643.; 26. V. de Spinadel. The metallic means family and multifractal spectra, Nonlinear Analysis 1999, 36: 721–745.; 27. Bradley S. A geometric connection between generalized Fibonacci sequences and nearly golden sections, Fibonacci Quarterly 2000, 38.2: 174–179. –fq.math.ca/Scanned/38-2/bradley.pdf.; 28. Stakhov A. Generalized Golden Sections and a new approach to the geometric definition of a number, Ukrainian Mathematical Journal 2004, 56 (8): 1143–1150.; 29. Stakhov A. The Generalized Principle of the Golden Section and its Applications in Mathematics, Science and Engineering, Chaos, Solitons & Fractals 2005, 26(2): 263–289.; 30. Stakhov A. Fundamentals of a new kind of Mathematics based on the Golden Section, Chaos, Solitons & Fractals 2005, 27(5): 1124–1146.; 31. V. de Spinadel. The Metallic means Family and Art Aplimat, Journal of Appl. Mathematics 2010, 3(1): 53–64.; 36. Stakhov A. The Golden Section and Modern Harmony Mathmatics, Applications of Fibonacci numbers, Vol. 7 (Graz, 1996), Kluwer Academic Publishers, 1998, pp. 393–399.; 39. Koshy T. Fibonacci and Lucas numbers with application. A Wiley-Interscience Publication: New York, 2001.; 40. Bodnar O. The Golden Section and Non-Euclidean Geometry in Science and Art. Lviv: Publishing House "Ukrainian Technologies", 2005 (Ukrainian).; 42. Schneider R. A Golden Product Identity for e, Mathematics Magazine 2014, 87(2): 132–134.; Kosobutskyy P. Mathematical methods for CAD: the method of proportional division of thewhole into two unequal parts / P. Kosobutskyy, M. Karkulovska, A. Morgulis // Вісник Національного університету “Львівська політехніка”. Серія: Комп’ютерні системи проектування теорія і практика. — Львів : Видавництво Львівської політехніки, 2018. — № 908. — С. 75–89.; https://ena.lpnu.ua/handle/ntb/46919; Kosobutskyy P. Mathematical methods for CAD: the method of proportional division of thewhole into two unequal parts / P. Kosobutskyy, M. Karkulovska, A. Morgulis // Visnyk Natsionalnoho universytetu "Lvivska politekhnika". Serie: Kompiuterni systemy proektuvannia teoriia i praktyka. — Lviv : Vydavnytstvo Lvivskoi politekhniky, 2018. — No 908. — P. 75–89.

    Διαθεσιμότητα: https://ena.lpnu.ua/handle/ntb/46919