Series On Knots And Everything
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Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science
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.<b>Contents:</b> <ul><li>Foundations of the Constructive (Algorithmic) Measurement Theory</li><li>Principle of Asymmetry of Measurement and Fibonacci Algorithms of Measurement</li><li>Evolution of Numeral Systems</li><li>Bergman's System and 'Golden' Number Theory</li><li>The 'Golden' Ternary Mirror-Symmetrical Arithmetic</li><li>Fibonacci <i>p</i>-Codes and Fibonacci Arithmetic for Mission-Critical Applications</li><li>Codes of the Golden <i>p</i>-Proportions</li></ul><br><b>Readership:</b> High school, college and university students, teachers, professionals, scientists and investors interested in history of mathematics, Fibonacci numbers, golden section and their generalization.Babylonian Numeral System;Golden Section;Platonic Solids;Pythagoreanism And Pythagorean Mathem's;Classical Mathematics;Mathematics of Harmony;“Golden” Paradigm;Fibonacci Numbers;Philosophy0<b>Key Features:</b><ul><li>In the world literature there is only one book, devoted to the «Mathematics of Harmony»</li><li>Scornful attitude towards the «school» and applied arithmetic and its problems</li><li>Can serve as the explanation of the fact why in the number theory attention was not given to numeral systems</li><li>The great interest was again shown to the methods of the representation of numbers and new computer arithmetic</li><li>The ternary computer «Setun», designed by the Russian engineer Nikolay Brousentsov on the basis of the ternary system, was the brightest example</li><li>Mathematics again returned to the period of its origin, when the numeral systems were as one of the main subjects of the ancient mathematics</li></ul>
Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science
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.<b>Contents:</b> <ul><li>Mathematics of Harmony as a Prerequisite for the 'Golden' Revolution in Mathematics and Computer Science</li><li>The 'Golden' Hyperbolic Functions as the 'Golden' Paradigm Shift to the 'Golden' Non-Euclidean Geometry</li><li>Applications of the Symmetric Hyperbolic Fibonacci and Lucas Functions</li><li>Theory of Fibonacci and Lucas λ-Numbers and Its Applications</li><li>Hilbert Problems: General Information</li><li>Beauty and Aesthetics of Harmony Mathematics</li><li>Epilogue</li></ul> remove <p><b>Sample Chapter(s)</b><br><a href='http://www.worldscientific.com/doi/suppl/10.1142/11645/suppl_file/11645_preface.pdf'>Preface to the Three-Volume Book</a><br><a href='http://www.worldscientific.com/doi/suppl/10.1142/11645/suppl_file/11645_intro.pdf'>Introduction</a><br><a href='http://www.worldscientific.com/doi/pdf/10.1142/9789811213502_0001'>Chapter 1. Mathematics of Harmony as a Prerequisite for the 'Golden' Revolution in Mathematics and Computer Science</a><br><br></p> /remove <br><b>Readership:</b> High school, college and university students, teachers, professionals, scientists and investors interested in history of mathematics, Fibonacci numbers, golden section and their generalization.Babylonian Numeral System;Golden Section;Platonic Solids;Pythagoreanism and Pythagorean Mathem's;Classical Mathematics;Mathematics of Harmony;“Golden” Paradigm;Fibonacci Numbers;Philosophy0<b>Key Features:</b><ul><li>The present 3-volume book will promote to the implementation of these «harmonic ideas» into modern science and education</li><li>Will lead to more deep understanding of the ancient conception of the «Universe Harmony,»</li><li>The creation of the «harmonious» society of the future</li></ul>
