Alexey Stakhov's Books

"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant

By: Alexey Stakhov,Samuil Aranson

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"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant

By: Alexey Stakhov,Samuil Aranson

This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of 'recursive' hyperbolic functions based on the 'Mathematics of Harmony,' and the 'golden,' 'silver,' and other 'metallic' proportions. Then, these theories are used to derive an original solution to Hilbert's Fourth Problem for hyperbolic and spherical geometries. On this journey, the book describes the 'golden' qualitative theory of dynamical systems based on 'metallic' proportions. Finally, it presents a solution to a Millennium Problem by developing the Fibonacci special theory of relativity as an original physical-mathematical solution for the fine-structure constant. It is intended for a wide audience who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems, dynamical systems, and Millennium Problems.See Press Release: Application of the mathematics of harmony - Golden non-Euclidean geometry in modern math

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307

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World Scientific

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ISBN 10

9814678317

ISBN 13

9789814678315

The Mathematics of Harmony

From Euclid to Contemporary Mathematics and Computer Science

By: Alexey Stakhov

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The Mathematics of Harmony

From Euclid to Contemporary Mathematics and Computer Science

By: Alexey Stakhov

Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science.

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745

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World Scientific

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ISBN 10

9812775838

ISBN 13

9789812775832

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic

By: Alexey Stakhov

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Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic

By: Alexey Stakhov

Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

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Page Count

331

Publisher

World Scientific

Published Date

ISBN 10

9811213488

ISBN 13

9789811213489

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids

By: Alexey Stakhov

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Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids

By: Alexey Stakhov

Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

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247

Publisher

World Scientific

Published Date

ISBN 10

9811206384

ISBN 13

9789811206382

Mathematics Of Harmony: From Euclid To Contemporary Mathematics And Computer Science

By: Alexey Stakhov

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Mathematics Of Harmony: From Euclid To Contemporary Mathematics And Computer Science

By: Alexey Stakhov

Assisted by Scott Olsen (Central Florida Community College, USA) This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the “Mathematics of Harmony,” a new interdisciplinary direction of modern science. This direction has its origins in “The Elements” of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the “golden” algebraic equations, the generalized Binet formulas, Fibonacci and “golden” matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and “golden” matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

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745

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World Scientific

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ISBN 10

9814472573

ISBN 13

9789814472579

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences

By: Alexey Stakhov

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Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences

By: Alexey Stakhov

Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

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244

Publisher

World Scientific

Published Date

ISBN 10

9811213518

ISBN 13

9789811213519

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic

By: Alexey Stakhov

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Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic

By: Alexey Stakhov

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Page Count

331

Publisher

World Scientific

Published Date

ISBN 10

9811213488

ISBN 13

9789811213489

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids

By: Alexey Stakhov

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Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids

By: Alexey Stakhov

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247

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World Scientific

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ISBN 10

9811206384

ISBN 13

9789811206382

"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant

By: Alexey Stakhov,Samuil Aranson

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"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant

By: Alexey Stakhov,Samuil Aranson

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307

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World Scientific

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ISBN 10

9814678317

ISBN 13

9789814678315

Numeral Systems With Irrational Bases For Mission-critical Applications

By: Alexey Stakhov

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Numeral Systems With Irrational Bases For Mission-critical Applications

By: Alexey Stakhov

This volume is the result of the author's many-years of research in this field. These results were presented in the author's two books, Introduction to the Algorithmic Measurement Theory (Moscow, Soviet Radio, 1977), and Codes of the Golden Proportion (Moscow, Radio and Communications, 1984), which had not been translated into English and are therefore not known to English-speaking audience. This volume sets forth new informational and arithmetical fundamentals of computer and measurement systems based on Fibonacci p-codes and codes of the golden p-proportions, and also on Bergman's system and 'golden' ternary mirror-symmetrical arithmetic. The book presents some new historical hypotheses concerning the origin of the Egyptian calendar and the Babylonian numeral system with base 60 (dodecahedral hypothesis), as well as about the origin of the Mayan's calendar and their numeral system with base 20 (icosahedral hypothesis). The book is intended for the college and university level. The book will also be of interest to all researchers, who use the golden ratio and Fibonacci numbers in their subject areas, and to all readers who are interested to the history of mathematics.

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Page Count

285

Publisher

World Scientific

Published Date

ISBN 10

9813228636

ISBN 13

9789813228634

Mathematics of Harmony As a New Interdisciplinary Direction of Modern Science - Volume 1: the Golden Section, Fibonacci Numbers, Pascal Triangle, and Platonic Solids

By: Alexey Stakhov

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Mathematics of Harmony As a New Interdisciplinary Direction of Modern Science - Volume 1: the Golden Section, Fibonacci Numbers, Pascal Triangle, and Platonic Solids

By: Alexey Stakhov

Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and "Golden" Paradigm of Modern Science. "Mathematics of Harmony" rises in its origin to the "harmonic ideas" of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the "Universe Harmony," the main conception of ancient Greek science, and implementation of this conception to modern science and education. This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony," a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic). The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

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Page Count

248

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9811207100

ISBN 13

9789811207105

Mathematics of Harmony As a New Interdisciplinary Direction and Golden Paradigm of Modern Science-Volume 3: the Golden Paradigm of Modern Science: Prerequisite for the Golden Revolution in Mathematics, Computer Science, and Theoretical Natural Scienc

By: Alexey Stakhov

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Mathematics of Harmony As a New Interdisciplinary Direction and Golden Paradigm of Modern Science-Volume 3: the Golden Paradigm of Modern Science: Prerequisite for the Golden Revolution in Mathematics, Computer Science, and Theoretical Natural Scienc

By: Alexey Stakhov

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Page Count

196

Publisher

Knots and Everything

Published Date

ISBN 10

9811213496

ISBN 13

9789811213496

Book's by Alexey Stakhov

"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant

"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant

The Mathematics of Harmony

The Mathematics of Harmony

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids

Mathematics Of Harmony: From Euclid To Contemporary Mathematics And Computer Science

Mathematics Of Harmony: From Euclid To Contemporary Mathematics And Computer Science

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids

"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant

"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant

Numeral Systems With Irrational Bases For Mission-critical Applications

Numeral Systems With Irrational Bases For Mission-critical Applications

Mathematics of Harmony As a New Interdisciplinary Direction of Modern Science - Volume 1: the Golden Section, Fibonacci Numbers, Pascal Triangle, and Platonic Solids

Mathematics of Harmony As a New Interdisciplinary Direction of Modern Science - Volume 1: the Golden Section, Fibonacci Numbers, Pascal Triangle, and Platonic Solids

Mathematics of Harmony As a New Interdisciplinary Direction and Golden Paradigm of Modern Science-Volume 3: the Golden Paradigm of Modern Science: Prerequisite for the Golden Revolution in Mathematics, Computer Science, and Theoretical Natural Scienc

Mathematics of Harmony As a New Interdisciplinary Direction and Golden Paradigm of Modern Science-Volume 3: the Golden Paradigm of Modern Science: Prerequisite for the Golden Revolution in Mathematics, Computer Science, and Theoretical Natural Scienc

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