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...
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In this paper, we shall prove that if the domination number of G is at most 2, then P (G,λ) is zero-free in the interval (1, β), where β = 2 + 1 6 3 √ 12 √ 93− 108− 1 6 3 √ 12 √ 93 + 108 = 1.317672196 · · · , and P (G, β) = 0 for some graph G with domination number 2. We also show that if ∆(G) ≥ v(G) − 2, then P (G,λ) is zero-free in the interval (1, β′), where β′ = 5 3 + 1 6 3 √ 12 √ 69− 44− 1...
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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...
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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 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.
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ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2009
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm0901120a