The mathematics of harmony : from Euclid to contemporary mathematics and computer science

著者

    • Stakhov, A. P. (Alekseĭ Petrovich)
    • Olsen, Scott Anthony

書誌事項

The mathematics of harmony : from Euclid to contemporary mathematics and computer science

Alexey Stakhov ; assisted by Scott Olsen

（Series on knots and everything, v. 22）

World Scientific, c2009

  • : hard

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注記

Includes bibliographical references (p. 661-674) and index

内容説明・目次

内容説明

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 “Mathematics of Harmony,” a new interdisciplinary direction of modern science. This direction has its origins in “The Elements” 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 “golden” algebraic equations, the generalized Binet formulas, Fibonacci and “golden” 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 “golden” 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.

目次

  • The Golden Section
  • Fibonacci and Lucas Numbers
  • Regular Polyhedrons
  • Generalizations of Fibonacci Numbers and the Golden Section
  • Hyperbolic Fibonacci and Lucas Functions
  • Fibonacci and the "Golden" Matrices Algorithmic Measurement Theory
  • Fibonacci Computers
  • Number Systems with Irrational Radices
  • Ternary Mirror-Symmetrical Arithmetic
  • Fibonacci and "Golden" Matrices and a New Theory of Coding
  • Appendices: The Most Important Mathematical Results of the Harmony Mathematics
  • The Museum of Harmony and the Golden Section.

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