04167nam 2200625 450 991083073030332120170816115416.01-283-33204-397866133320421-118-03306-X1-118-03131-8(CKB)2670000000133090(EBL)695119(OCoLC)768204521(SSID)ssj0000613298(PQKBManifestationID)11412201(PQKBTitleCode)TC0000613298(PQKBWorkID)10585002(PQKB)11346118(MiAaPQ)EBC695119(PPN)234990295(EXLCZ)99267000000013309020160816h20012001 uy 0engur|n|---|||||txtccrFibonacci and Lucas numbers with applications /Thomas KoshyNew York, New York :John Wiley & Sons, Inc.,2001.©20011 online resource (676 p.)Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts"A Wiley-Interscience Publication."0-471-39969-8 Includes bibliographical references and index.Fibonacci 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 Properties17. 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 Periodicity36. 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; ReferencesSolutions to Odd-Numbered ExercisesIndexThe 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 Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and TractsFibonacci numbersLucas numbersFibonacci numbers.Lucas numbers.512.72Koshy Thomas601527MiAaPQMiAaPQMiAaPQBOOK9910830730303321Fibonacci and Lucas numbers with applications1020303UNINA