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, 2013 The golden ratio, or phi (φ = 1.6180339887...), is a ratio that has interested mathematicians as well as artists, philosophers, and many others for over 2,000 years.
Williams, Emily
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Generalized golden ratios of ternary alphabets
Journal of the European Mathematical Society, 2011 Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions.
KOMORNIK V +2 more
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Three-Dimensional Brownian Motion and the Golden Ratio Rule [PDF]
Let X =(Xt)t=0 be a transient diffusion processin (0,8) with the diffusion coeffcient s> 0 and the scale function L such that Xt ?8 as t ?8 ,let It denote its running minimum for t = 0, and let ? denote the time of its ultimate minimum I8 .Setting c(i,x)=
Hardy Hulley +2 more
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Golden ratio: Concepts, misconceptions and applications [PDF]
, 1998 This paper is an exposition on misconceptions and applications of the Golden Ratio. This is taken from the two articles Independent Sets and the Golden Ratio by William Staton and Clifton Wingard and Misconception About the Golden Ratio by George ...
Megia, Margarita Catherine O.
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The human heart: Application of the golden ratio and angle [PDF]
, 2011 The golden ratio, or golden mean, of 1.618 is a proportion known since antiquity to be the most aesthetically pleasing and has been used repeatedly in art and architecture.
Ashraf W. Khir +13 more
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Golden ratio algorithms for variational inequalities [PDF]
Mathematical Programming, 2019 The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a linesearch. Thus, each iteration of the method requires only one evaluation of a monotone operator $F$ and a proximal ...
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, 2018 A systematic comprehensive empirical test of the golden ratio principle with various ...
Sascha Topolinski, Thorsten Michael Erle
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Golden Ratio Function: Similarity Fields in the Vector Space
MathematicsIn this work, we generalize and describe the golden ratio in multi-dimensional vector spaces. We also introduce the concept of the law of similarity for multidimensional vectors.
Artyom Grigoryan, Meruzhan Grigoryan
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Golden Gait: An Optimization Theory Perspective on Human and Humanoid Walking
Frontiers in Neurorobotics, 2017 Human walking is a complex task which includes hundreds of muscles, bones and joints working together to deliver harmonic movements with the need of finding equilibrium between moving forward and maintaining stability.
Marco Iosa +2 more
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Golden ratio nets and sequences
Functiones et Approximatio Commentarii MathematiciIn this paper we introduce and study nets and sequences constructed in an irrational base, focusing on the case of a base given by the golden ratio $ϕ$. We provide a complete framework to study equidistribution properties of nets in base $ϕ$, which among other things requires the introduction of a new concept of prime elementary intervals which differ ...
Kirk, Nathan +2 more
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