↑ The golden ratio can be derived by the quadratic formula, by starting with the first number as 1, then solving for 2nd number x, where the ratios (x + 1)/x = x/1 or (multiplying by x) yields: x + 1 = x2, or thus a quadratic equation: x2 − x − 1 = 0. Then, by the quadratic formula, for positive x = (−b + √(b2 − 4ac))/(2a) with a = 1, b = −1, c = −1, the solution for x is: (−(−1) + √((−1)2 − 4·1·(−1)))/(2·1) or (1 + √(5))/2.
↑ Livio, Mario (2002). The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Broadway Books. ISBN 0-7679-0815-5.
↑ Piotr Sadowski, The Knight on His Quest: Symbolic Patterns of Transition in Sir Gawain and the Green Knight, Cranbury NJ: Associated University Presses, 1996
↑ Richard A Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, 1997
↑ 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
↑ Pacioli, Luca. De divina proportione, Luca Paganinem de Paganinus de Brescia (Antonio Capella) 1509, Venice.
