Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science. Alexey Stakhov. Читать онлайн. Newlib. NEWLIB.NET

Автор: Alexey Stakhov
Издательство: Ingram
Серия: Series On Knots And Everything
Жанр произведения: Математика
Год издания: 0
isbn: 9789811206382
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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

      

Series on Knots and Everything — Vol. 65

       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

      Alexey Stakhov

      International Club of the Golden Section, Canada & Academy of Trinitarism, Russia

       Published by

      World Scientific Publishing Co. Pte. Ltd.

      5 Toh Tuck Link, Singapore 596224

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

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

      Library of Congress Control Number: 2020010957

       British Library Cataloguing-in-Publication Data

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

      Series on Knots and Everything — Vol. 65 MATHEMATICS OF HARMONY AS A NEW INTERDISCIPLINARY DIRECTION AND “GOLDEN” PARADIGM OF MODERN SCIENCEVolume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, and Platonic Solids

      Copyright © 2020 by World Scientific Publishing Co. Pte. Ltd.

       All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.

      For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

      ISBN 978-981-120-710-5 (hardcover)

      ISBN 978-981-120-637-5 (ebook for institutions)

      ISBN 978-981-120-638-2 (ebook for individuals)

      For any available supplementary material, please visit

      https://www.worldscientific.com/worldscibooks/10.1142/11445#t=suppl

      Desk Editor: Liu Yumeng

      Typeset by Stallion Press

      Email: [email protected]

      Printed in Singapore

      In fond memory of Yuri Alekseevich Mitropolskiy and Alexander Andreevich Volkov

       Contents

       Preface to the Three-Volume Book

       Introduction

       About the Author

       Acknowledgments

       Chapter 1. The Golden Section: History and Applications

       1.1 The Idea of the Universeal Harmony in Ancient Greek Science

       1.2 The Golden Section in Euclid’s Elements

       1.3 Proclus Hypothesis and New View on Classic Mathematics and Mathematics of Harmony

       1.4 Some Simplest Mathematical Properties of the Golden Ratio

       1.5 The Golden Ratio and Chain Fractions

       1.6 Equations of the Golden Proportion of the Nth Degree

       1.7 Geometric Figures Associated with the Golden Section

       1.8 The Golden Section in Nature

       1.9 The Golden Section in Cheops Pyramid

       1.10 The Golden Section in Ancient Greek Culture

       1.11 Golden Section in the Art of the Renaissance

       Chapter 2. Fibonacci and Lucas Numbers

       2.1 A History of the Fibonacci Numbers

       2.2 The Sums of the Consecutive Fibonacci Numbers

       2.3 Cassini’s Formula

       2.4 Lucas Numbers

       2.5 Binet’s Formulas

       2.6 Steinhaus’s “Iron Table”

       2.7 Pythagorean Triangles and Their Presentation Through Fibonacci and Lucas Numbers

       2.8 Fibonacci Numbers in Nature

       2.9 Fibonacci Numbers and Solution of Hilbert 10th Problem

       2.10 Turing and Fibonacci Numbers

       2.11 Role of the Fibonacci Numbers Theory in Modern Mathematics

       Chapter 3. Pascal Triangle, Fibonacci p-Numbers and Golden p-Proportions

       3.1 Binomial Theorem

       3.2 Pascal Triangle

       3.3 Diagonal Sums of Pascal’s Triangle and Fibonacci p-Numbers

       3.4 The Extended Fibonacci p-Numbers