The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
By M. Livio. 2002
685 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/a96a1110a9510f46ac6032ff7e270f51cc2fbd83
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Citations in the corpus
- Universal spin-momentum locking of evanescent waves (2015, background): “which is the minimum allowable ratio of the permittivities for CTIR to occur, and curiously, it can also be identified as the golden ratio [15].”
- Applications of the Golden Ratio on Riemannian Manifolds (2009, unknown): “2 Using an explicit expression for the Fibonacci sequence (Binet’s formula [12]): fn = φ − (1 − φ) √ 5 , (2.”
- Introduction: Number as Inventive Frontier (2010, background): “But the main image has been topological (see Leach, 1971) and structure-building (as in Lévi-Strauss, 1963), with much less numerical reference (except in certain systems approaches such as by J. Clyde Mitchell).”
- Neuronal Reward and Decision Signals: From Theories to Data. (2015, unknown): “A good example is Canaletto’s Grand Canal (FIGURE 2) whose particular beauty is based on physical geometric properties, like the off-center Golden Ratio position reflecting a Fibonacci sequence (320).”
- On k-Fibonacci sequences and polynomials and their derivatives (2009, background): “There is a huge interest of modern science in the application of the Golden Section and Fibonacci numbers [1–10].”
- Electromagnetic field optimization: A physics-inspired metaheuristic optimization algorithm (2016, background): “The first phenomenon is the attraction–repulsion forces among electromagnets with different polarities, and the second phenomenon is a nature-inspired ratio called the golden ratio [23], which is also known as god’s fingerprint.”
- On the 3-dimensional k-Fibonacci spirals (2008, unknown): “F k;nþm 1⁄4 F k;nþ1F k;m þ F k;nF k;m 1 • If k 1⁄4 1, for the classical Fibonacci sequence is obtained: F nþm 1⁄4 F nþ1F m þ F nF m 1 (Honsberger’s formula [15]).”
- On generalized Fibonacci and Lucas polynomials (2009, background): “Introduction In modern science there is a huge interest in the theory and application of the Golden Section and Fibonacci numbers [1–34].”
- On the Fibonacci k-numbers (2007, background): “(2) is known as Livio’s formula [2].”
- Geometrical Substantiation of Phi , the Golden Ratio and the Baroque of Nature, Architecture, Design and Engineering (2012, background): “International Journal of Arts 2011; 1(1): 1-22 17 structure, (b) Parthenon, (c) Notre Dame in Paris, (d) United Nation building, (e) Canadian National (CN) Tower, (f) Sculpture called The Seed designed by Peter Randall, (g) Australian sculptor Andrew Rogers's 50-ton stone and gold sculpture, entitle”
- An Optimal Radial Profile Order Based on the Golden Ratio for Time-Resolved MRI (2007, background): “1 (b)] [17] . b) If the number of profiles equals a Fibonacci number, only two different azimuthal gaps occur.”