Fibonacci and Lucas numbers with applications / / Thomas Koshy

• Autore: Koshy Thomas
• Pubblicazione: New York, New York : , : John Wiley & Sons, Inc., , 2001; ©2001
• Descrizione fisica: 1 online resource (676 p.)
• Disciplina: 512.72
• Soggetto topico: Fibonacci numbers; Lucas numbers
• Note generali: "A Wiley-Interscience Publication."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 ; 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 ; 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; 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 ; Solutions to Odd-Numbered ExercisesIndex
• 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
• Titolo autorizzato: Fibonacci and Lucas numbers with applications
• ISBN: 1-283-33204-3; 9786613332042; 1-118-03306-X; 1-118-03131-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910141196603321
• Lo trovi qui: Univ. Federico II
• Serie: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts