The mathematics of harmony :: from Euclid to contemporary mathematics and computer science /
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 directio...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2009.
|
| Schriftenreihe: | K & E series on knots and everything ;
v. 22. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | 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 resource (xlix, 694 pages) : illustrations (some color) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812775832 9812775838 |
Internformat
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| 245 | 1 | 4 | |a The mathematics of harmony : |b from Euclid to contemporary mathematics and computer science / |c Alexey Stakhov ; assisted by Scott Olsen. |
| 260 | |a Singapore ; |a Hackensack, NJ : |b World Scientific, |c ©2009. | ||
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| 490 | 1 | |a K & E series on knots and everything ; |v v. 22 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a 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. | |
| 520 | |a 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 | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Fibonacci numbers. |0 http://id.loc.gov/authorities/subjects/sh85048028 | |
| 650 | 0 | |a Golden section. |0 http://id.loc.gov/authorities/subjects/sh85055763 | |
| 650 | 0 | |a Mathematics |x History. | |
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| 650 | 6 | |a Suites de Fibonacci. | |
| 650 | 6 | |a Nombre d'or. | |
| 650 | 6 | |a Mathématiques |x Histoire. | |
| 650 | 6 | |a Informatique. | |
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| 650 | 7 | |a golden section. |2 aat | |
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| author | Stakhov, A. P. (Alekseĭ Petrovich) |
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| contents | 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. |
| ctrlnum | (OCoLC)670429766 |
| dewey-full | 512.7/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/2 |
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| dewey-sort | 3512.7 12 |
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| discipline | Mathematik |
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| genre | History fast |
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| id | ZDB-4-EBA-ocn670429766 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:37:01Z |
| institution | BVB |
| isbn | 9789812775832 9812775838 |
| language | English |
| oclc_num | 670429766 |
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| series | K & E series on knots and everything ; |
| series2 | K & E series on knots and everything ; |
| spelling | Stakhov, A. P. (Alekseĭ Petrovich) https://id.oclc.org/worldcat/entity/E39PBJtH3jrkFYwgKBPWP3bTpP http://id.loc.gov/authorities/names/n85154102 The mathematics of harmony : from Euclid to contemporary mathematics and computer science / Alexey Stakhov ; assisted by Scott Olsen. Singapore ; Hackensack, NJ : World Scientific, ©2009. 1 online resource (xlix, 694 pages) : illustrations (some color) text txt rdacontent computer c rdamedia online resource 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 Print version record. Fibonacci numbers. http://id.loc.gov/authorities/subjects/sh85048028 Golden section. http://id.loc.gov/authorities/subjects/sh85055763 Mathematics History. Computer science. http://id.loc.gov/authorities/subjects/sh89003285 Electronic Data Processing https://id.nlm.nih.gov/mesh/D001330 Suites de Fibonacci. Nombre d'or. Mathématiques Histoire. Informatique. Fibonacci numbers. aat golden section. aat MATHEMATICS Number Theory. bisacsh Computer science fast Fibonacci numbers fast Golden section fast Mathematics fast Goldener Schnitt. idsbb Fibonacci-Folge. idsbb mathematik. idsbb Ästhetik Mathematik. idsbb Mathematik Ästhetik. idsbb History fast Olsen, Scott Anthony. Print version: Stakhov, A.P. (Alekseĭ Petrovich). Mathematics of harmony. Singapore ; Hackensack, NJ : World Scientific, ©2009 981277582X (DLC) 2009021159 (OCoLC)185032768 K & E series on knots and everything ; v. 22. http://id.loc.gov/authorities/names/n91052105 |
| spellingShingle | Stakhov, A. P. (Alekseĭ Petrovich) The mathematics of harmony : from Euclid to contemporary mathematics and computer science / K & E series on knots and everything ; 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. Fibonacci numbers. http://id.loc.gov/authorities/subjects/sh85048028 Golden section. http://id.loc.gov/authorities/subjects/sh85055763 Mathematics History. Computer science. http://id.loc.gov/authorities/subjects/sh89003285 Electronic Data Processing https://id.nlm.nih.gov/mesh/D001330 Suites de Fibonacci. Nombre d'or. Mathématiques Histoire. Informatique. Fibonacci numbers. aat golden section. aat MATHEMATICS Number Theory. bisacsh Computer science fast Fibonacci numbers fast Golden section fast Mathematics fast Goldener Schnitt. idsbb Fibonacci-Folge. idsbb mathematik. idsbb Ästhetik Mathematik. idsbb Mathematik Ästhetik. idsbb |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048028 http://id.loc.gov/authorities/subjects/sh85055763 http://id.loc.gov/authorities/subjects/sh89003285 https://id.nlm.nih.gov/mesh/D001330 |
| 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 | mathematics of harmony from euclid to contemporary mathematics and computer science |
| title_sub | from Euclid to contemporary mathematics and computer science / |
| topic | Fibonacci numbers. http://id.loc.gov/authorities/subjects/sh85048028 Golden section. http://id.loc.gov/authorities/subjects/sh85055763 Mathematics History. Computer science. http://id.loc.gov/authorities/subjects/sh89003285 Electronic Data Processing https://id.nlm.nih.gov/mesh/D001330 Suites de Fibonacci. Nombre d'or. Mathématiques Histoire. Informatique. Fibonacci numbers. aat golden section. aat MATHEMATICS Number Theory. bisacsh Computer science fast Fibonacci numbers fast Golden section fast Mathematics fast Goldener Schnitt. idsbb Fibonacci-Folge. idsbb mathematik. idsbb Ästhetik Mathematik. idsbb Mathematik Ästhetik. idsbb |
| topic_facet | Fibonacci numbers. Golden section. Mathematics History. Computer science. Electronic Data Processing Suites de Fibonacci. Nombre d'or. Mathématiques Histoire. Informatique. golden section. MATHEMATICS Number Theory. Computer science Fibonacci numbers Golden section Mathematics Goldener Schnitt. Fibonacci-Folge. mathematik. Ästhetik Mathematik. Mathematik Ästhetik. History |
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