The mathematics of harmony: from Euclid to contemporary mathematics and computer science
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2009
|
| Schriftenreihe: | K & E series on knots and everything
v. 22 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and index Three "key" problems of mathematics on the stage of its origin -- 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 -- Dirac's principle of mathematical beauty and the mathematics of harmony : clarifying the origins and development of mathematics -- Appendix : Museum of harmony and the golden section 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 |
| Beschreibung: | 1 Online-Ressource (xlix, 694 p.) |
| ISBN: | 9789812775825 9789812775832 981277582X 9812775838 |
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Datensatz im Suchindex
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| author | Stakhov, A. P., (Alekseĭ Petrovich) |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/2 |
| dewey-search | 512.7/2 |
| dewey-sort | 3512.7 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | Geschichte gnd |
| era_facet | Geschichte |
| format | Electronic eBook |
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| spelling | Stakhov, A. P., (Alekseĭ Petrovich) Verfasser aut The mathematics of harmony from Euclid to contemporary mathematics and computer science Alexey Stakhov ; assisted by Scott Olsen Singapore World Scientific c2009 1 Online-Ressource (xlix, 694 p.) txt rdacontent c rdamedia cr rdacarrier K & E series on knots and everything v. 22 Includes bibliographical references and index Three "key" problems of mathematics on the stage of its origin -- 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 -- Dirac's principle of mathematical beauty and the mathematics of harmony : clarifying the origins and development of mathematics -- Appendix : Museum of harmony and the golden section 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 Geschichte gnd rswk-swf MATHEMATICS / Number Theory bisacsh Goldener Schnitt idsbb Fibonacci-Folge idsbb mathematik idsbb Ästhetik / Mathematik idsbb Mathematik / Ästhetik idsbb Computer science fast Fibonacci numbers fast Golden section fast Mathematics fast Geschichte Informatik Mathematik Fibonacci numbers Golden section Mathematics History Computer science Mathematik (DE-588)4037944-9 gnd rswk-swf Goldener Schnitt (DE-588)4021529-5 gnd rswk-swf Fibonacci-Folge (DE-588)4249138-1 gnd rswk-swf Fibonacci-Folge (DE-588)4249138-1 s Goldener Schnitt (DE-588)4021529-5 s Mathematik (DE-588)4037944-9 s Geschichte z 1\p DE-604 Olsen, Scott Anthony Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340565 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stakhov, A. P., (Alekseĭ Petrovich) The mathematics of harmony from Euclid to contemporary mathematics and computer science MATHEMATICS / Number Theory bisacsh Goldener Schnitt idsbb Fibonacci-Folge idsbb mathematik idsbb Ästhetik / Mathematik idsbb Mathematik / Ästhetik idsbb Computer science fast Fibonacci numbers fast Golden section fast Mathematics fast Geschichte Informatik Mathematik Fibonacci numbers Golden section Mathematics History Computer science Mathematik (DE-588)4037944-9 gnd Goldener Schnitt (DE-588)4021529-5 gnd Fibonacci-Folge (DE-588)4249138-1 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4021529-5 (DE-588)4249138-1 |
| title | The mathematics of harmony from Euclid to contemporary mathematics and computer science |
| title_auth | The mathematics of harmony from Euclid to contemporary mathematics and computer science |
| title_exact_search | The mathematics of harmony from Euclid to contemporary mathematics and computer science |
| title_full | The mathematics of harmony from Euclid to contemporary mathematics and computer science Alexey Stakhov ; assisted by Scott Olsen |
| title_fullStr | The mathematics of harmony from Euclid to contemporary mathematics and computer science Alexey Stakhov ; assisted by Scott Olsen |
| title_full_unstemmed | The mathematics of harmony from Euclid to contemporary mathematics and computer science Alexey Stakhov ; assisted by Scott Olsen |
| title_short | The mathematics of harmony |
| title_sort | the mathematics of harmony from euclid to contemporary mathematics and computer science |
| title_sub | from Euclid to contemporary mathematics and computer science |
| topic | MATHEMATICS / Number Theory bisacsh Goldener Schnitt idsbb Fibonacci-Folge idsbb mathematik idsbb Ästhetik / Mathematik idsbb Mathematik / Ästhetik idsbb Computer science fast Fibonacci numbers fast Golden section fast Mathematics fast Geschichte Informatik Mathematik Fibonacci numbers Golden section Mathematics History Computer science Mathematik (DE-588)4037944-9 gnd Goldener Schnitt (DE-588)4021529-5 gnd Fibonacci-Folge (DE-588)4249138-1 gnd |
| topic_facet | MATHEMATICS / Number Theory Goldener Schnitt Fibonacci-Folge mathematik Ästhetik / Mathematik Mathematik / Ästhetik Computer science Fibonacci numbers Golden section Mathematics Geschichte Informatik Mathematik Mathematics History |
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