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Built in ability to detect and correct up to** 99.98%** of all errors, not only in code but also in arithmetic operations.

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Using Harmonic “redundant” number systems **reduces energy usage and heat generation by up to two times.**

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Possesses perfect** code coherence **and flawless transmission of serial data.

The **Harmonic Microchip** is the culminating result of over 50 years of work, 65 international patents, 130 Soviet invention certificates, 14 books, 500+ scientific publications.

The inventor behind this technology is **Professor Alexey Stakhov** the world authority on Nature’s Mathematics of Harmony, the Golden ratio and the Fibonacci numbers.

This new revolutionary technology is based on new redundant number systems the Fibonacci *p-*codes and codes of golden ratio *p*-proportions, it is the evolution of the binary code a step closer to nature, which provides these unique built in advantages. The technology still retains full compatibility with the classic binary systems as it is able to translate the code there for making it work seamlessly with all modern digital microelectronics.

The **Harmonic Microchip** is designed to be used in mission critical systems in these vital, global multi-billion dollar industries.

Opinions and reviews of international experts about Harmony Systems and Mathematics of Harmony

Scientific achievements of Ukrainian scientists are well known all over the world. **Alexey Stakhov, Professor of Vinnitsa State Technical University, Doctor of Engineering Sciences is one of the brightest representatives of Ukrainian science.** His scientific achievements in the field of Fibonacci numbers and the golden section and their applications, in particular, in the theory of harmonic systems, computer and measurement technology** can provide the basis for the revolutionary transformations of modern science, for the creation of new mathematical theories of natural sciences, fundamentally new computing and measurement systems.**

Research carried out in the Laboratory of Fault-tolerant Systems of the Ukrainian National Academy of Sciences (scientific supervisor Prof. Alexey Stakhov) have shown that based of the so-called Fibonacci and golden ratio codes **competitive measuring and computer systems can be created, which can exceed the current world level in reliability**.** These systems can be used for mission critical applications, where the need for their reliability is vital, such as in (control systems for space, energy, transport and other technological objects).**

Who is it that understands this driving principle behind all of Nature, perhaps better than anyone else alive? It is Alexey Stakhov! His new book, The Mathematics of Harmony, may well change the course of human history. No mathematical mind today, in my humble estimation, can match the depth, breadth of scope, and creativity of Alexey Stakhov. As it turns out, these recent scientific developments in physics, cosmology, mathematics, aesthetics, nanotechnology, computer programming and design, artificial intelligence, and biology, have refocused attention on a revival of interest in ancient Pythagorean ideas about the numerical harmonics of the Universe, including both its macrocosmic and microcosmic levels. Thus a door has been opened wide inviting a fundamental reassessment of Plato’s Cosmology,Euclid’s Elements and the very history and future development of mathematics itself.

**Special Design and Technological Bureau “Module” under the direction of Alexey Stakhov** of the Vinnitsa Polytechnic Institute in cooperation with the **Ukrainian Academy of Sciences** is conducting research and designing **highly reliable on-board processors, computers, measurement and control systems based on the “Harmonic” Fibonacci code (the invention of Alexey Stakhov)** in the interests of **Ministry of General Engineering (Soviet Rockets Ministry).**

This research direction has got **wide international recognition**; it is protected by** over 100 copyright certificates of the USSR** and** 65 international patents** and relates to the category of priority research. It aims is to elevate various separate areas of **Soviet digital computing technology to the global level.**

**Boris Paton - **President of the Ukrainian Academy of Sciences, **V.D. Parkhomenko - **Minister of Higher and Secondary Education of Ukraine, **W.H. Doguzhiev - **Minister of General Engineering of the USSR, **I.S. Nayashkov - **Chairman of the Soviet State Committee on Inventions and Patenting

Dear Alexey Stakhov,

I congratulate you with publication of the article “Brousentsov’s ternary principle, Bergman’s number system and ternary mirror-symmetrical arithmetic” (The Computer Journal 2002, Vol. 45, No. 2)

Your ternary mirror-symmetrical arithmetic is so interesting that I plan to post the information about this unusual computer arithmetic in the new edition of my book “The Art of Computer Programming”

Professor Stakhov has written a book that may well change not only the way we view the history of mathematics, but the future development of mathematics in its application to the natural sciences and computer design. This book is the result of the author’s four decades of research in the field of Fibonacci numbers and the Golden Mean (also called the Golden Ratio or the Golden Section) and their applications. The volume contains chapters on the history of mathematics, the generalized Fibonaccis and Lucas numbers, the generalized golden proportions, the golden algebraic equations, the generalized Binet formulas, Fibonacci and golden matrices, and hyperbolic models. Stakhov suggests applications of number systems (Bergman’s numeral system) with irrational radices in computers, coding theory, cryptography and mobil phone design, because irrational numbers are nothing else than commands for mathematical operations in space and time.

**Codes of the Golden р-proportions.**

With the concept of the golden *р-*proportion, Stakhov introduced a new definition of real number in the form of:

\(A=\sum\limits_{i}{{{a}_{i}}\tau _{p}^{i}\quad }\left( {{a}_{i}}\in \left\{ 0,1 \right\} \right).\)

He named this sum the “Code of the golden *р-*proportion.” Stakhov has proven that this concept, which is an elaboration of the well known “Newton’s definition” of real numbers, **can be used for the creation of a new theory of real numbers.** Furthermore, he has proven that this result **could be used for the creation of new computer arithmetic and new computers – “Harmonic” Fibonacci computers**. Stakhov not only introduced the idea of “Harmonic” Fibonacci computers, but he also organised the engineering projects for the creation of such computer prototypes in the Vinnitsa Polytechnic Institute from 1977-1995. **65 patents for inventions in the field of Fibonacci computers have been issued by the state patent offices of the United States, Japan, England, France, Germany, Canada, and other countries; these patents have confirmed the significance of Ukrainian science—and of Professor Stakhov—in this important computer direction.**

HARMONY SYSTEMS | Digital technology inspired by Natures mathematics of Harmony | Patent pending | Copyright 2013 ©