منابع مشابه
A 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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In this paper, we give a pedagogical introduction to several beautiful formulas discovered by Ramanujan. Using these results, we evaluate a Ramanujan-type integral formula. The result can be expressed in terms of the Golden Ratio.
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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. 1. GENERALIZED GOLDEN RATIOS There have been many generalizations of the number known as golden ratio or golden section, φ = 1+ √ 5 2 . Examples are G.A. Moore’s golden numbers [10] and S. Bradley’s nearly golden sections [5] (see also...
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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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ژورنال
عنوان ژورنال: Nature
سال: 2010
ISSN: 0028-0836,1476-4687
DOI: 10.1038/464362a