Mathematics of Harmony (Series on Knots and Everything) by Alexey Stakhov, Scott Olsen

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By Alexey Stakhov, Scott Olsen

Professor Stakhov has written a e-book that could good swap not just the best way we view the heritage of arithmetic, however the destiny improvement of arithmetic in its program to the usual sciences and computing device layout. This e-book is the results of the author's 4 a long time of analysis within the box of Fibonacci numbers and the Golden suggest (also known as the Golden Ratio or the Golden part) and their functions. the amount comprises chapters at the heritage of arithmetic, the generalized Fibonaccis and Lucas numbers, the generalized golden proportions, the golden algebraic equations, the generalized Binet formulation, Fibonacci and golden matrices, and hyperbolic versions. Stakhov indicates functions of quantity platforms (Bergman's numeral method) with irrational radices in pcs, coding conception, cryptography and mobil telephone layout, simply because irrational numbers are not anything else than instructions for mathematical operations in house and time, see the place arithmetic Comes From: How the Embodied brain Brings arithmetic into Being.

Stakhov, of Russian and Ukrainian heritage, now residing in Toronto, Canada, is a phenomenal member of a minority of scientists, who has discovered that the Golden suggest and its expression via Pascal's Triangle, Fibonacci and Lucas quantity lies on the very heart of the inventive precept of nature itself. contemporary medical advancements in physics, chemistry and cosmology have refocused cognizance to the mathematical homes of the Golden suggest and its that means at the macrocosmic and microcosmic levels.

However, no clinical paintings can ever be whole: Stakhov isn't conscious of a few advancements in theoretical chemistry via Jan Boeyens, see quantity idea and the Periodicity of subject and Chemistry from First ideas, aiding the elemental position of the golden suggest. additionally the e-book a brand new form of technology is stuffed with Pascal's Triangles!

Until now, from my standpoint "From Golden suggest to Chaos" (printed in Argentina and, it's a pity, now not on supply by means of amazon.com) by way of Vera de Spinadel is or used to be the main complex e-book at the value of the Golden suggest. Stakhov cites this e-book, yet doesn't check with renormalization and the Kolmogorov-Arnold-Moser theorem, within which the Golden suggest performs a task, too.

Until now, our brains and desktops have a rather various structure. notwithstanding, by means of encoding and deciphering the knowledge entropy of a process no different wave may be extra optimum than a wavelet containing the Golden suggest and its arithmetic itself. certainly, in accordance with empirical info, the paper "The golden suggest as clock cycle of mind waves", released in Chaos, Solitons and Fractals 18 (2003) 643-652, means that our mind makes use of those merits of "The arithmetic of Harmony"! And already Roopun, A. ok. et al., Frontiers in Neuroscience 2 (2008) 145-154, proven empirically this end of the monstrous position of the Golden suggest in our processing of data. Does our mind even paintings at the foundation of a Ternary Mirror-Symmetrical Numeral procedure, as invented via Stakhov?

The caliber of paper and print of this publication is way above general. as a minimum you'll purchase a e-book, with a view to locate its position within the historical past of science.

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Scott Olsen, the American philosopher and prominent researcher in the golden mean and author of the book The Golden Section: Nature’s Greatest Secret (2006), for his invaluable assistance in the scientific and English editing of my book. Also, I would like to express my greatest gratitude to the Russian businessman and scientist Dr. Ivan Raylyan, a great enthusiast of the Golden Section, for his Acknowledgements xli financial assistance, which provided me with all of the best technology, infor mational tools, and pecuniary means to produce a camera ready manuscript.

2. , τn −1 , τn ,... 18) has very interesting properties. 18), that is, τn = τ × τn −1 . 18) has the prop erty of “additivity” because each element is equal to the sum of the two pre ceding elements. 15) is characteristic only for the geometrical progression with the denominator τ, and such geometrical pro gression is named the Golden Progression, Golden Series or Golden Powers. 18) among other geometrical progressions, and this fact is a reason for the wide spread prevalence of the golden logarithmic spiral in forms and structures of nature.

Scott Olsen, the American philosopher and prominent researcher in the golden mean and author of the book The Golden Section: Nature’s Greatest Secret (2006), for his invaluable assistance in the scientific and English editing of my book. Also, I would like to express my greatest gratitude to the Russian businessman and scientist Dr. Ivan Raylyan, a great enthusiast of the Golden Section, for his Acknowledgements xli financial assistance, which provided me with all of the best technology, infor mational tools, and pecuniary means to produce a camera ready manuscript.

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