Fibonacci and Lucas Numbers with Applications, Volume 1
eBook - ePub

Fibonacci and Lucas Numbers with Applications, Volume 1

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

Fibonacci and Lucas Numbers with Applications, Volume 1

About this book

Praise for the First Edition

" …beautiful and well worth the reading … with many exercises and a good bibliography, this book will fascinate both students and teachers." Mathematics Teacher

Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many opportunities to explore and experiment.

In addition, the book includes a historical survey of the development of Fibonacci and Lucas numbers, with biographical sketches of important figures in the field. Each chapter features a wealth of examples, as well as numeric and theoretical exercises that avoid using extensive and time-consuming proofs of theorems. The Second Edition offers new opportunities to illustrate and expand on various problem-solving skills and techniques. In addition, the book features:

• A clear, comprehensive introduction to one of the most fascinating topics in mathematics, including links to graph theory, matrices, geometry, the stock market, and the Golden Ratio

• Abundant examples, exercises, and properties throughout, with a wide range of difficulty and sophistication

• Numeric puzzles based on Fibonacci numbers, as well as popular geometric paradoxes, and a glossary of symbols and fundamental properties from the theory of numbers

• A wide range of applications in many disciplines, including architecture, biology, chemistry, electrical engineering, physics, physiology, and neurophysiology

The Second Edition is appropriate for upper-undergraduate and graduate-level courses on the history of mathematics, combinatorics, and number theory. The book is also a valuable resource for undergraduate research courses, independent study projects, and senior/graduate theses, as well as a useful resource for computer scientists, physicists, biologists, and electrical engineers.

Thomas Koshy, PhD, is Professor Emeritus of Mathematics at Framingham State University in Massachusetts and author of several books and numerous articles on mathematics. His work has been recognized by the Association of American Publishers, and he has received many awards, including the Distinguished Faculty of the Year. Dr. Koshy received his PhD in Algebraic Coding Theory from Boston University.

"Anyone who loves mathematical puzzles, number theory, and Fibonacci numbers will treasure this book. Dr. Koshy has compiled Fibonacci lore from diverse sources into one understandable and intriguing volume, [interweaving] a historical flavor into an array of applications." Marjorie Bicknell-Johnson

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Yes, you can access Fibonacci and Lucas Numbers with Applications, Volume 1 by Thomas Koshy in PDF and/or ePUB format, as well as other popular books in Mathematics & History & Philosophy of Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover
  2. TITLE PAGE
  3. COPYRIGHT
  4. TABLE OF CONTENTS
  5. DEDICATION
  6. LIST OF SYMBOLS
  7. PREFACE
  8. CHAPTER 1: LEONARDO FIBONACCI
  9. CHAPTER 2: FIBONACCI NUMBERS
  10. CHAPTER 3: FIBONACCI NUMBERS IN NATURE
  11. CHAPTER 4: ADDITIONAL FIBONACCI AND LUCAS OCCURRENCES
  12. CHAPTER 5: FIBONACCI AND LUCAS IDENTITIES
  13. CHAPTER 6: GEOMETRIC ILLUSTRATIONS AND PARADOXES
  14. CHAPTER 7: GIBONACCI NUMBERS
  15. CHAPTER 8: ADDITIONAL FIBONACCI AND LUCAS FORMULAS
  16. CHAPTER 9: THE EUCLIDEAN ALGORITHM
  17. CHAPTER 10: DIVISIBILITY PROPERTIES
  18. CHAPTER 11: PASCAL'S TRIANGLE
  19. CHAPTER 12: PASCAL-LIKE TRIANGLES
  20. CHAPTER 13: RECURRENCES AND GENERATING FUNCTIONS
  21. CHAPTER 14: COMBINATORIAL MODELS I
  22. CHAPTER 15: HOSOYA'S TRIANGLE
  23. CHAPTER 16: THE GOLDEN RATIO
  24. CHAPTER 17: GOLDEN TRIANGLES AND RECTANGLES
  25. CHAPTER 18: FIGEOMETRY
  26. CHAPTER 19: CONTINUED FRACTIONS
  27. CHAPTER 20: FIBONACCI MATRICES
  28. CHAPTER 21: GRAPH-THEORETIC MODELS I
  29. CHAPTER 22: FIBONACCI DETERMINANTS
  30. CHAPTER 23: FIBONACCI AND LUCAS CONGRUENCES
  31. CHAPTER 24: FIBONACCI AND LUCAS SERIES
  32. CHAPTER 25: WEIGHTED FIBONACCI AND LUCAS SUMS
  33. CHAPTER 26: FIBONOMETRY I
  34. CHAPTER 27: COMPLETENESS THEOREMS
  35. CHAPTER 28: THE KNAPSACK PROBLEM
  36. CHAPTER 29: FIBONACCI AND LUCAS SUBSCRIPTS
  37. CHAPTER 30: FIBONACCI AND THE COMPLEX PLANE
  38. APPENDIX 1: FUNDAMENTALS
  39. APPENDIX 2: THE FIRST 100 FIBONACCI AND LUCAS NUMBERS
  40. APPENDIX 3: THE FIRST 100 FIBONACCI NUMBERS AND THEIR PRIME FACTORIZATIONS
  41. APPENDIX 4: THE FIRST 100 LUCAS NUMBERS AND THEIR PRIME FACTORIZATIONS
  42. ABBREVIATIONS
  43. REFERENCES
  44. SOLUTIONS TO ODD-NUMBERED EXERCISES
  45. INDEX
  46. PURE AND APPLIED MATHEMATICS
  47. END USER LICENSE AGREEMENT