Spirals and the Golden Section

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منابع مشابه

A Generalization of the Golden Section

13. K. Jordan. Chapters on the Classical Calculus of Probability. Akademiai Kiadb, Budapest, 1972. 14. P. A. MacMahon. Combinatory Analysis, Vols. I and II. New York: Chelsea, 1960. 15. G. P. Patil & J. K. Wani. "On Certain Structural Properties of the Logarithmic Series Distribution and the First Type Stirling Distribution." Sankhya, Series A, 27 (1965):271-180. 16. J. Riordan. An Introduction...

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The golden section, ϕ = (1 + √5)/2 = 1.618... and its companion ϕ = 1/ϕ = ϕ -1 = 0.618..., are irrational numbers which for centuries were believed to confer aesthetic appeal. In line with the presence of golden sectioning in natural growth patterns, recent EEG recordings show an absence of coherence between brain frequencies related by the golden ratio, suggesting the potential relevance of th...

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The relation between the discrete time Lainiotis filter on the one side and the golden section and the Fibonacci sequence on the other is established. As far as the random walk system is concerned, the relation between the Lainiotis filter and the golden section is derived through the Riccati equation since the steady state estimation error covariance is related to the golden section. The relat...

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My paper has two parts. First, I talk about the golden rule. After introducing the rule and its global importance, I explain why many scholars dismiss it as a vague proverb that leads to absurdities when we try to formulate it clearly. I defend the golden rule against such objections. Second, I talk about the golden rule in Persia and Islam; I consider Persian sources (Muslim and non-Muslim) an...

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On Machin’s formula with Powers of the Golden Section

In this note, we find all solutions of the equation π 4 = a arctan(φκ)+ b arctan(φ`), in integers κ and ` and rational numbers a and b, where φ is the golden section. MSC: 11D45, 11D85, 11R04, 11R29.

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ژورنال

عنوان ژورنال: Nexus Network Journal

سال: 2002

ISSN: 1590-5896,1522-4600

DOI: 10.1007/s00004-001-0005-x