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79,647
TENTH ROOTS AND THE GOLDEN RATIO
, 1984
"... The ratio of the radius of a circle and a side of the inscribed regular decagon equals the golden ratio T. In the complex plane the spines of a regular decagon inscribed in a circle of unit radius are the vector representations of the complex tenth roots of1, if the decagon is appropriately turned. ..."
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The ratio of the radius of a circle and a side of the inscribed regular decagon equals the golden ratio T. In the complex plane the spines of a regular decagon inscribed in a circle of unit radius are the vector representations of the complex tenth roots of1, if the decagon is appropriately turned. These
Golden Ratio in Quantum Mechanics
"... The experimental discovery of the golden mean in quantum mechanics by the Helmholtz group(R. Coldea, et al., Golden ratio discovered in a quantum world, Science, 8 January,2010) is discussed. The direct and important relation of this discovery with El Naschie’s Einfinity theory is outlined. ..."
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Cited by 1 (0 self)
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The experimental discovery of the golden mean in quantum mechanics by the Helmholtz group(R. Coldea, et al., Golden ratio discovered in a quantum world, Science, 8 January,2010) is discussed. The direct and important relation of this discovery with El Naschie’s Einfinity theory is outlined.
A golden ratio notation . . .
, 1996
"... Several methods to perform exact computations on real numbers have been proposed in the literature. In some of these methods real numbers are represented by infinite (lazy) strings of digits. It is a well known fact that, when this approach is taken, the standard digit notation cannot be used. New f ..."
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digits (0 and 1) and the golden ratio as base. This choice is motivated by the pleasing properties enjoyed...
SPANNING FORESTS AND THE GOLDEN RATIO
, 2007
"... For a graph G, let fij be the number of spanning rooted forests in which vertex j belongs to a tree rooted at i. In this paper, we show that for a path graph, fij’s can be expressed as products of Fibonacci numbers; for a cycle graph, they are products of Fibonacci numbers and Lucas numbers. The dou ..."
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Cited by 7 (4 self)
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that for the path graphs and the socalled Tcaterpillars, some diagonal entries of F (which measure the selfconnectivity of vertices) converge to φ −1 or to 1 − φ −1, where φ is the golden ratio, as the number of vertices goes to infinity. Thereby, in the asymptotic, the corresponding vertices can
Directed Percolation and the Golden Ratio
, 2001
"... Abstract. Applying the theory of YangLee zeros to nonequilibrium critical phenomena, we investigate the properties of a directed bond percolation process for a complex percolation parameter p. It is shown that for the Golden Ratio p = (1 ± √ 5)/2 and for p = 2 the survival probability of a cluster ..."
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Abstract. Applying the theory of YangLee zeros to nonequilibrium critical phenomena, we investigate the properties of a directed bond percolation process for a complex percolation parameter p. It is shown that for the Golden Ratio p = (1 ± √ 5)/2 and for p = 2 the survival probability of a
1. GENERALIZED GOLDEN RATIOS
, 2005
"... We propose a generalization of the golden section based on division in mean and extreme ratio. The associated integer sequences have many interesting properties. ..."
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We propose a generalization of the golden section based on division in mean and extreme ratio. The associated integer sequences have many interesting properties.
The Generalized Equation of the Golden Ratio
, 1972
"... which arises in Li Kung Shaw f s mathematical model of human life induces a new development in that historically famous topic of mathematics and magic, the Golden Section Ratio. Here, S represents a m a n ' s service hours and h his work hours. The equation (1) arises as the condition for the h ..."
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which arises in Li Kung Shaw f s mathematical model of human life induces a new development in that historically famous topic of mathematics and magic, the Golden Section Ratio. Here, S represents a m a n ' s service hours and h his work hours. The equation (1) arises as the condition
Results 1  10
of
79,647