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[null,"1.","Record Nr.",null,"UNINA9910830730303321"]
[null,null,"Autore",null,"Koshy Thomas"]
[null,null,"Titolo",null,"Fibonacci and Lucas numbers with applications / / Thomas Koshy"]
[null,null,"Pubbl/distr/stampa",null,"New York, New York : , : John Wiley & Sons, Inc., , 2001"]
[{"$nulls":4},"©2001"]
[null,null,"ISBN",null,"1-283-33204-3"]
[{"$nulls":4},"9786613332042"]
[{"$nulls":4},"1-118-03306-X"]
[{"$nulls":4},"1-118-03131-8"]
[null,null,"Descrizione fisica",null,"1 online resource (676 p.)"]
[null,null,"Collana",null,"Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts"]
[null,null,"Disciplina",null,"512.72"]
[null,null,"Soggetti",null,"Fibonacci numbers"]
[{"$nulls":4},"Lucas numbers"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","\"A Wiley-Interscience Publication.\""]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Fibonacci and Lucas Numbers with Applications; CONTENTS; Preface; List of Symbols; 1. Leonardo Fibonacci; 2. The Rabbit Problem; 3. Fibonacci Numbers in Nature; 4. Fibonacci Numbers: Additional Occurrences; 5. Fibonacci and Lucas Identities; 6. Geometric Paradoxes; 7. Generalized Fibonacci Numbers; 8. Additional Fibonacci and Lucas Formulas; 9. The Euclidean Algorithm; 10. Solving Recurrence Relations; 11. Completeness Theorems; 12. Pascal's Triangle; 13. Pascal-Like Triangles; 14. Additional Pascal-Like Triangles; 15. Hosoya's Triangle; 16. Divisibility Properties"]
[{"$nulls":4},"17. 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"]
[{"$nulls":4},"36. Fibonacci and Lucas Series37. Fibonacci Polynomials; 38. Lucas Polynomials; 39. Jacobsthal Polynomials; 40. Zeros of Fibonacci and Lucas Polynomials; 41. Morgan-Voyce Polynomials; 42. Fibonometry; "]
[{"$nulls":4},"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"]
[{"$nulls":4},"Solutions to Odd-Numbered ExercisesIndex"]
[null,null,null,"Sommario/riassunto","The 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"]