The Mathematics Of Harmony
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The Mathematics Of Harmony
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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2009
The Mathematics Of Harmony written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
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."
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
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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2020-05-05
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 written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.
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.
The Mathematics Of Harmony
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language : en
Publisher:
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The Mathematics Of Harmony written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
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
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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2020-09-03
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 written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-03 with Mathematics categories.
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.
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
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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2020-09-03
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 written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-03 with Mathematics categories.
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.
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
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Author : Alexey Stakhov
language : en
Publisher:
Release Date : 2020
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 written by Alexey Stakhov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Electronic books categories.
The Mathematics Of Harmony And Hilbert S Fourth Problem
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Author : Alexey Stakhov
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2014-04
The Mathematics Of Harmony And Hilbert S Fourth Problem written by Alexey Stakhov and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04 with categories.
A unique book that turns our notions about Euclid's Elements and non-Euclidean geometry. Proclus' hypothesis leads to the new view on the mathematics history, starting from Euclid. According to this hypothesis, Euclid's main goal, while writing the Elements, was to create a complete geometric theory of "Platonic solids," which are associated in the ancient Greek science with the Universe Harmony. Euclid's Elements is a source for the Classical Mathematics and the Mathematics of Harmony based on the "golden ratio" and "Platonic solids." The Mathematics of Harmony, as a new interdisciplinary direction of modern science, is a reflection of the "harmonic ideas" by Pythagoras and Plato in modern science and mathematics. New classes of hyperbolic and spherical Fibonacci functions, based on the "golden proportion" and its generalization - the "metallic proportions," underlie the original solution of Hilbert's Fourth Problem for hyperbolic and spherical geometry. The challenge searching for new hyperbolic and spherical worlds of Nature follows from this solution. The "golden" hyperbolic geometry with the base 1.618 ("Bodnar geometry") underlies botanical phenomenon of phyllotaxis.
Mathematics Of Harmony As A New Interdisciplinary Direction Of Modern Science Volume 1 The Golden Section Fibonacci Numbers Pascal Triangle And Platonic Solids
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Author : Alexey Stakhov
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020
Mathematics Of Harmony As A New Interdisciplinary Direction Of Modern Science Volume 1 The Golden Section Fibonacci Numbers Pascal Triangle And Platonic Solids written by Alexey Stakhov and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
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.
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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Author : Alexey Stakhov
language : en
Publisher: Knots and Everything
Release Date : 2020
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 written by Alexey Stakhov and has been published by Knots and Everything this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
"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"--
The Golden Non Euclidean Geometry
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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2016-07-14
The Golden Non Euclidean Geometry written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-14 with Mathematics categories.
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. Contents:The Golden Ratio, Fibonacci Numbers, and the "Golden" Hyperbolic Fibonacci and Lucas FunctionsThe Mathematics of Harmony and General Theory of Recursive Hyperbolic FunctionsHyperbolic and Spherical Solutions of Hilbert's Fourth Problem: The Way to the Recursive Non-Euclidean GeometriesIntroduction to the "Golden" Qualitative Theory of Dynamical Systems Based on the Mathematics of HarmonyThe Basic Stages of the Mathematical Solution to the Fine-Structure Constant Problem as a Physical Millennium ProblemAppendix: From the "Golden" Geometry to the Multiverse Readership: Advanced undergraduate and graduate students in mathematics and theoretical physics, mathematicians and scientists of different specializations interested in history of mathematics and new mathematical ideas.