منابع مشابه
The golden ratio and aesthetics
Mario Livio is a scientist and self−proclaimed "art fanatic" who owns many hundreds of art books. Recently, he combined his passions for science and art in two popular books, The Accelerating Universe, which appeared in 2000, and The Golden Ratio, reviewed in this issue of Plus. The former book discusses "beauty" as an essential ingredient in fundamental theories of the universe. The latter dis...
متن کاملSimilar Triangles, Another Trace of the Golden Ratio
In this paper we investigate similar triangles which are not congruent but have two pair congruent sides. We show that greatest lower bound of values for similarity ratio of such triangles is golden ratio. For right triangles, we prove that the supremum of values for similarity ratio is the square root of the golden ratio.
متن کاملDirected Percolation and the Golden Ratio
Applying the theory of Yang-Lee 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 can be computed exactly. PACS numbers: 02.50.-r,64.60.Ak,05.50.+q Directed percolation (DP) is an anisotropi...
متن کاملSpanning forests and the golden ratio
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, the fij’s can be expressed as the products of Fibonacci numbers; for a cycle, they are products of Fibonacci and Lucas numbers. The doubly stochastic graph matrix is the matrix F = (fij)n×n f , where f is the total number of spanning rooted for...
متن کاملA Golden Ratio Notation for the Real
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 innnite (lazy) strings of digits. It is a well known fact that, when this approach is taken, the standard digit notation cannot be used. New forms of digit notations are necessary. The usual solution to this representation problem consists ...
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ژورنال
عنوان ژورنال: Journal of Modern Physics
سال: 2016
ISSN: 2153-1196,2153-120X
DOI: 10.4236/jmp.2016.714171