The Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science (Google eBook)

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World Scientific, Sep 11, 2009 - Computer science - 745 pages
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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."
  

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Contents

Three Key Problems of Mathematics on the Stage
Acknowledgements xxxix
Classical Golden Mean Fibonacci
1
xvi
6
Fibonacci and Lucas Numbers
60
xiv
83
Regular Polyhedrons
137
Generalizations of Fibonacci Numbers and the Golden Mean
186
Application in Computer Science
359
Fibonacci Computers
416
Codes of the Golden Proportion
476
Ternary Mirror Symmetrical Arithmetic
523
xviii
569
Epilogue Diracs Principle of Mathematical Beauty and the Mathematics
615
Three Key Problems of Mathematics and a New Approach
632
the Golden Information
646

Hyperbolic Fibonacci and Lucas Functions
255
StakhovRozin Definition
277
Fibonacci and Golden Matrices
317
Matrices and their Powers
343
References
661
Museum of Harmony and Golden Section
675
Copyright

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