نسبت طلایی
ارجاعات

1 2  "Compendium of Mathematical Symbols". Math Vault (به انگلیسی). 2020-03-01. Retrieved 2020-08-10.
↑  Weisstein, Eric W. "Golden Ratio". mathworld.wolfram.com (به انگلیسی). Retrieved 2020-08-10.
1 2   A001622
↑  Livio 2003, pp. 3, 81.
↑  Dunlap, Richard A. , The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, 1997
↑  Euclid, Elements, Book 6, Definition 3.
↑  Summerson John, Heavenly Mansions: And Other Essays on Architecture (New York: W.W. Norton, 1963) p.  37. "And the same applies in architecture, to the rectangles representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design."
↑  Jay Hambidge, Dynamic Symmetry: The Greek Vase, New Haven CT: Yale University Press, 1920
↑  William Lidwell, Kritina Holden, Jill Butler, Universal Principles of Design: A Cross-Disciplinary Reference, Gloucester MA: Rockport Publishers, 2003
1 2  Pacioli, Luca. De divina proportione, Luca Paganinem de Paganinus de Brescia (Antonio Capella) 1509, Venice.
↑  Strogatz, Steven (September 24, 2012). "Me, Myself, and Math: Proportion Control". The New York Times.
↑  Weisstein, Eric W. "Golden Ratio Conjugate". MathWorld.
↑  Livio 2003, p. 6.
↑  Livio 2003, p. 4: "... line division, which Euclid defined for … purely geometrical purposes ..."
↑  Livio 2003, pp. 7–8.
↑  Livio 2003, pp. 4–5.
↑  Livio 2003, p. 78.
↑  Hemenway, Priya (2005). Divine Proportion: Phi In Art, Nature, and Science. New York: Sterling. pp. 20–21. ISBN 978-1-4027-3522-6.
↑  Livio 2003, p. 3.
↑  Richard Fitzpatrick (translator) (2007). Euclid's Elements of Geometry. p. 156. ISBN 978-0-615-17984-1. {{cite book}}: |author= has generic name (help)
↑  Livio 2003, pp. 88–96.
↑  Livio 2003, pp. 131–132.
↑  Baravalle, H. V. (1948). "The geometry of the pentagon and the golden section". Mathematics Teacher. 41: 22–31.
↑  Livio 2003, p. 141.
↑  Schreiber, Peter (1995). "A Supplement to J. Shallit's Paper "Origins of the Analysis of the Euclidean Algorithm"". Historia Mathematica. 22 (4): 422–424. doi:10.1006/hmat.1995.1033.
↑  Livio 2003, pp. 151–152.
↑  "The Golden Ratio". The MacTutor History of Mathematics archive. Retrieved 2007-09-18.
↑  Fink, Karl; Beman, Wooster Woodruff; Smith, David Eugene (1903). A Brief History of Mathematics: An Authorized Translation of Dr. Karl Fink's Geschichte der Elementar-Mathematik (2nd ed.). Chicago: Open Court Publishing Co. p. 223.
↑  Weisstein, Eric W. "Binet's Fibonacci Number Formula". MathWorld.
↑  Herz-Fischler, Roger (1987). A Mathematical History of Division in Extreme and Mean Ratio. Wilfrid Laurier University Press. ISBN 978-0-88920-152-1.
↑  Posamentier, Alfred S.; Lehmann, Ingmar (2011). The Glorious Golden Ratio. Prometheus Books. p. 8. ISBN 978-1-61614-424-1.
↑  Posamentier, Alfred S.; Lehmann, Ingmar (2011). The Glorious Golden Ratio. Prometheus Books. p. 285. ISBN 978-1-61614-424-1.
↑  Cook, Theodore Andrea (1914). The Curves of Life. London: Constable and Company Ltd. p. 420.
↑  Barr, Mark (1929). "Parameters of beauty". Architecture (NY). Vol. 60. p. 325. Reprinted: "Parameters of beauty". Think. Vol. 10–11. International Business Machines Corporation. 1944.
↑  Livio 2003, p. 5.
↑  Weisstein, Eric W. "Golden Ratio". MathWorld.
↑  Gardner, Martin (2001). The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. W.W. Norton & Company. pp. 77, 88. ISBN 978-0-393-02023-6.
↑  Gerlin, Andrea (October 5, 2011). "Tecnion's Shechtman Wins Nobel in Chemistry for Quasicrystals Discovery". Bloomberg. Archived from the original on December 5, 2014. Retrieved January 4, 2019.
↑  Jaric, Marko V. (2012), Introduction to the Mathematics of Quasicrystals, Elsevier, p. x, ISBN 978-0-323-15947-0, Although at the time of the discovery of quasicrystals the theory of quasiperiodic functions had been known for nearly sixty years, it was the mathematics of aperiodic Penrose tilings, mostly developed by Nicolaas de Bruijn, that provided the major influence on the new field.
↑  Livio 2003, pp. 203–209.
↑  Goldman, Alan I.;  et al. (1996). "Quasicrystalline Materials". American Scientist. 84 (3): 230–241.