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

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      World Scientific Publishing Co. Pte. Ltd.

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       Library of Congress Cataloging-in-Publication Data

      Names: Stakhov, A. P. (Aleksei. 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. 68 | 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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       In fond memory of Yuri Alekseevich MitropolskiyandAlexander Andreevich Volkov

       Contents

       Preface to the Three-Volume Book

       Introduction

       About the Author

       Acknowledgments

       Chapter 1. Foundations of the Constructive (Algorithmic) Measurement Theory

       1.1 The Evolution of the Concept of “Measurement” in Mathematics

       1.2 Axioms of Eudoxus–Archimedes and Cantor

       1.3 The Problem of Infinity in Mathematics

       1.4 Criticism of the Cantor Theory of Infinite Sets

       1.5 Constructive Approach to the Creation of the Mathematical Measurement Theory

       1.6 The “Indicatory” Model of Measurement

       1.7 The Concept of the Optimal Measurement Algorithm

       1.8 Classical Measurement Algorithms

       1.9 Optimal (n, k, 0)-Algorithms

       1.10 Optimal (n, k, 1)-Algorithms Based on Arithmetic Square

       Chapter 2. Principle of Asymmetry of Measurement and Fibonacci Algorithms of Measurement

       2.1 Bachet–Mendeleev Problem

       2.2 Asymmetry Principle of Measurement

       2.3 A New Formulation of Bachet–Mendeleev Problem

       2.4 Synthesis of the Optimal Fibonacci’s Algorithm ofMeasurement

       2.5 Example of the Fibonacci Algorithm for the Case p = 1

       2.6 The Main Result of the Algorithmic Measurement Theory

       2.7 Isomorphism Between “Lever Balances” and “Rabbits Reproduction”

       2.8 Isomorphism Between the Algorithmic Theory