By Alexey Stakhov, Scott Olsen

Professor Stakhov has written a ebook which can good swap not just the best way we view the historical past 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 referred to as the Golden Ratio or the Golden part) and their functions. the amount includes chapters at the background 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 types. Stakhov indicates purposes of quantity platforms (Bergman's numeral approach) with irrational radices in desktops, coding conception, cryptography and mobil mobilephone 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 an exceptional 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 artistic precept of nature itself. fresh clinical advancements in physics, chemistry and cosmology have refocused awareness to the mathematical houses of the Golden suggest and its that means at the macrocosmic and microcosmic levels.

However, no medical paintings can ever be entire: Stakhov isn't really conscious of a few advancements in theoretical chemistry by means of Jan Boeyens, see quantity concept and the Periodicity of topic and Chemistry from First rules, assisting the elemental function of the golden suggest. additionally the publication a brand new type of technological know-how is filled with Pascal's Triangles!

Until now, from my viewpoint "From Golden suggest to Chaos" (printed in Argentina and, it's a pity, no longer on provide by way of amazon.com) by way of Vera de Spinadel is or used to be the main complicated ebook at the value of the Golden suggest. Stakhov cites this ebook, yet doesn't discuss with renormalization and the Kolmogorov-Arnold-Moser theorem, during which the Golden suggest performs a task, too.

Until now, our brains and pcs have a relatively diversified structure. even though, through encoding and deciphering the data entropy of a procedure no different wave may be extra optimum than a wavelet containing the Golden suggest and its arithmetic itself. certainly, according to empirical information, 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 benefits 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 vast position of the Golden suggest in our processing of knowledge. 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 e-book is much above typical. at least you'll purchase a ebook, with the intention to locate its position within the historical past of science.

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**Additional info for Mathematics of Harmony (Series on Knots and Everything) (Series in Knots and Everything)**

**Sample text**

Dunlap [38], Scott Olsen [54], Mohammed S. El Nashie [60 72], and other scientists had influenced the author’s research in this field. “Harmony Mathematics,” in its origin, goes back to the Euclidean problem of “division in the extreme and mean ratio” (the golden section) [40]. Harmony Mathematics is a continuation of the traditional “Fibonacci numbers theory” [13, 16, 28]. What are the purposes of this new mathematical theory? Similar to “classical mathematics,” which is defined sometimes as the “science about mod els” [5], we can consider Harmony Mathematics as the “science about the models of harmonic processes” in the world surrounding us.

The Main Goal of the Present Book It seems that the dramatic history of the DEMR (the golden section) that continued over several millennia has ended as a great triumph for the golden section in the beginning of the 21st century. Many outstanding scientific dis coveries that are based on the golden section (quasi crystals, fullerenes , “gold en” genomatrices and so on) gave reason to conclude that the golden section may be considered as some kind of “metaphysical knowledge,” “pre num ber,” or “universal code of Nature,” which could become the basis for the future development of science; particularly, theoretical physics, genetics, and computer science.

The 13 books of The Elements are dedicated to the knowledge of geometry and arithmetic of the Euclidean epoch. From The Elements of Euclid, the following geometrical problem, which was named the problem of “Division in Extreme and Mean Ratio” (DEMR), came to us [40]. 11 (the area formulation of DEMR). To divide a line AB into two segments, a larger one AC and a smaller one CB so that: S ( AC ) = R ( AB,CB ) . 1) Note that S ( AC ) is the area of a square with a side AC and R ( AB,CB ) is the area of a rectangle with sides AB and CB.