Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science. Alexey Stakhov

       Published by

      World Scientific Publishing Co. Pte. Ltd.

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      USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601

      UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

       Library of Congress Cataloging-in-Publication Data

      Names: Stakhov, A. P. (Alekseĭ Petrovich), author.

      Title: Mathematics of harmony as a new interdisciplinary direction and

      “golden” paradigm of modern science / Alexey Stakhov.

      Description: Hackensack, New Jersey : World Scientific, [2020] | Series: Series on knots and

      everything, 0219-9769 ; vol. 69 | Includes bibliographical references. | Contents:

      Volume 1. The golden section, Fibonacci numbers, Pascal triangle, and Platonic solids --

      Volume 2. Algorithmic measurement theory, Fibonacci and golden arithmetic and

      ternary mirror-symmetrical arithmetic -- Volume 3. The “golden” paradigm of modern science.

      Identifiers: LCCN 2020010957 | ISBN 9789811207105 (v. 1 ; hardcover) |

      ISBN 9789811213465 (v. 2 ; hardcover) | ISBN 9789811206375 (v. 1 ; ebook) |

      ISBN 9789811213496 (v. 3 ; hardcover) | ISBN 9789811206382 (v. 1 ; ebook other) |

      ISBN 9789811213472 (v. 2 ; ebook) | ISBN 9789811213489 (v. 2 ; ebook other) |

      ISBN 9789811213502 (v. 3 ; ebook) | ISBN 9789811213519 (v. 3 ; ebook other)

      Subjects: LCSH: Fibonacci numbers. | Golden section. | Mathematics--History. | Science--Mathematics.

      Classification: LCC QA246.5 .S732 2020 | DDC 512.7/2--dc23

      LC record available at https://lccn.loc.gov/2020010957

       British Library Cataloguing-in-Publication Data

      A catalogue record for this book is available from the British Library.

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      Printed in Singapore

       In fond memory of Yuri Alekseevich MitropolskiyandAlexander Andreevich Volkov

       Contents

       Preface to the Three-Volume Book

       Introduction

       About the Author

       Acknowledgments

       Chapter 1.Mathematics of Harmony as a Prerequisite for the “Golden” Revolution in Mathematics and Computer Science

       1.1“Proclus Hypothesis” as a Prerequisite for the “Golden” Revolution in the History of Mathematics

       1.2The Paradigm Shift to the “Golden” Elementary Number Theory

       1.3Fibonacci Microprocessors as a Prerequisite for the “Golden” Paradigm Shift in Computer Science

       1.4Sergey Abachiev: Mathematics of Harmony Through the Eyes of the Historian and Expert of Methodology of Science

       Chapter 2.The “Golden” Hyperbolic Functions as the “Golden” Paradigm Shift to the “Golden” Non-Euclidean Geometry

       2.1The Concept of “Elementary Functions”

       2.2Conic Sections and Hyperbola

       2.3Hyperbolic Rotation

       2.4Trigonometric Functions