LEADER 04167nam 2200625 450 001 9910830730303321 005 20170816115416.0 010 $a1-283-33204-3 010 $a9786613332042 010 $a1-118-03306-X 010 $a1-118-03131-8 035 $a(CKB)2670000000133090 035 $a(EBL)695119 035 $a(OCoLC)768204521 035 $a(SSID)ssj0000613298 035 $a(PQKBManifestationID)11412201 035 $a(PQKBTitleCode)TC0000613298 035 $a(PQKBWorkID)10585002 035 $a(PQKB)11346118 035 $a(MiAaPQ)EBC695119 035 $a(PPN)234990295 035 $a(EXLCZ)992670000000133090 100 $a20160816h20012001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFibonacci and Lucas numbers with applications /$fThomas Koshy 210 1$aNew York, New York :$cJohn Wiley & Sons, Inc.,$d2001. 210 4$dİ2001 215 $a1 online resource (676 p.) 225 0 $aPure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts 300 $a"A Wiley-Interscience Publication." 311 $a0-471-39969-8 320 $aIncludes bibliographical references and index. 327 $aFibonacci and Lucas Numbers with Applications; CONTENTS; Preface; List of Symbols; 1. Leonardo Fibonacci; 2. The Rabbit Problem; 3. Fibonacci Numbers in Nature; 4. Fibonacci Numbers: Additional Occurrences; 5. Fibonacci and Lucas Identities; 6. Geometric Paradoxes; 7. Generalized Fibonacci Numbers; 8. Additional Fibonacci and Lucas Formulas; 9. The Euclidean Algorithm; 10. Solving Recurrence Relations; 11. Completeness Theorems; 12. Pascal's Triangle; 13. Pascal-Like Triangles; 14. Additional Pascal-Like Triangles; 15. Hosoya's Triangle; 16. Divisibility Properties 327 $a17. Generalized Fibonacci Numbers Revisited18. Generating Functions; 19. Generating Functions Revisited; 20. The Golden Ratio; 21. The Golden Ratio Revisited; 22. Golden Triangles; 23. Golden Rectangles; 24. Fibonacci Geometry; 25. Regular Pentagons; 26. The Golden Ellipse and Hyperbola; 27. Continued Fractions; 28. Weighted Fibonacci and Lucas Sums; 29. Fibonacci and Lucas Sums Revisited; 30. The Knapsack Problem; 31. Fibonacci Magic Squares; 32. Fibonacci Matrices; 33. Fibonacci Determinants; 34. Fibonacci and Lucas Congruences; 35. Fibonacci and Lucas Periodicity 327 $a36. Fibonacci and Lucas Series37. Fibonacci Polynomials; 38. Lucas Polynomials; 39. Jacobsthal Polynomials; 40. Zeros of Fibonacci and Lucas Polynomials; 41. Morgan-Voyce Polynomials; 42. Fibonometry; 43. Fibonacci and Lucas Subscripts; 44. Gaussian Fibonacci and Lucas Numbers; 45. Analytic Extensions; 46. Tribonacci Numbers; 47. Tribonacci Polynomials; Appendix; A.1. Fundamentals; A.2. The First 100 Fibonacci and Lucas Numbers; A.3. The First 100 Fibonacci Numbers and Their Prime Factorizations; A.4. The First 100 Lucas Numbers and Their Prime Factorizations; References 327 $aSolutions to Odd-Numbered ExercisesIndex 330 $aThe first comprehensive survey of mathematics' most fascinating number sequencesFibonacci and Lucas numbers have intrigued amateur and professional mathematicians for centuries. This volume represents the first attempt to compile a definitive history and authoritative analysis of these famous integer sequences, complete with a wealth of exciting applications, enlightening examples, and fun exercises that offer numerous opportunities for exploration and experimentation.The author has assembled a myriad of fascinating properties of both Fibonacci and Lucas numbers-as developed by a wide 410 0$aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 606 $aFibonacci numbers 606 $aLucas numbers 615 0$aFibonacci numbers. 615 0$aLucas numbers. 676 $a512.72 700 $aKoshy$b Thomas$0601527 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830730303321 996 $aFibonacci and Lucas numbers with applications$91020303 997 $aUNINA