LEADER 00000cam  2200613Ki 4500 
001    ocn670429766 
003    OCoLC 
005    20160518075331.4 
006    m     o  d         
007    cr cnu---unuuu 
008    101018s2009    si a    ob    001 0 eng d 
019    613658835 
020    9789812775832|q(electronic bk.) 
020    9812775838|q(electronic bk.) 
035    (OCoLC)670429766|z(OCoLC)613658835 
040    N$T|beng|epn|erda|cN$T|dLLB|dE7B|dYDXCP|dOCLCQ|dOCLCF
       |dNLGGC|dOCLCO|dOCLCQ 
049    GTKE 
050  4 QA246.5|b.S73 2009eb 
082 04 512.7/2|222 
100 1  Stakhov, A. P.|q(Alekseĭ Petrovich) 
245 14 The mathematics of harmony :|bfrom Euclid to contemporary 
       mathematics and computer science /|cAlexey Stakhov ; 
       assisted by Scott Olsen. 
264  1 Singapore ;|aHackensack, NJ :|bWorld Scientific,|c[2009] 
264  4 |c©2009 
300    1 online resource (xlix, 694 pages) :|billustrations (some
       color). 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
490 1  K & E series on knots and everything ;|vv. 22 
504    Includes bibliographical references and index. 
505 0  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    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  Print version record. 
650  0 Fibonacci numbers. 
650  0 Golden section. 
650  0 Mathematics|xHistory. 
650  0 Computer science. 
650  7 MATHEMATICS|xNumber Theory.|2bisacsh 
650  7 Computer science.|2fast|0(OCoLC)fst00872451 
650  7 Fibonacci numbers.|2fast|0(OCoLC)fst00923656 
650  7 Golden section.|2fast|0(OCoLC)fst00944571 
650  7 Mathematics.|2fast|0(OCoLC)fst01012163 
650  7 Goldener Schnitt.|2idsbb 
650  7 Fibonacci-Folge.|2idsbb 
650  7 mathematik.|2idsbb 
650  7 Ästhetik|xMathematik.|2idsbb 
650  7 Mathematik|xÄsthetik.|2idsbb 
655  7 History.|2fast|0(OCoLC)fst01411628 
700 1  Olsen, Scott Anthony. 
776 08 |iPrint version:|aStakhov, A.P. (Alekseĭ Petrovich).
       |tMathematics of harmony.|dSingapore ; Hackensack, NJ : 
       World Scientific, ©2009|z981277582X|w(DLC)  2009021159
       |w(OCoLC)185032768 
830  0 K & E series on knots and everything ;|vv. 22. 
914    ocn670429766 
994    93|bGTK