Pell and Pell–Lucas Numbers with Applications

Thomas Koshy (Autor)

Buch | Hardcover

431 Seiten

2014
Springer-Verlag New York Inc.
978-1-4614-8488-2 (ISBN)

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Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis, geometry, trigonometry, and various areas of discrete mathematics, number theory, graph theory, linear algebra, and combinatorics. Pell and Pell–Lucas numbers belong to an extended Fibonacci family as a powerful tool for extracting numerous interesting properties of a vast array of number sequences.

A key feature of this work is the historical flavor that is interwoven into the extensive and in-depth coverage of the subject. An interesting array of applications to combinatorics, graph theory, geometry, and intriguing mathematical puzzles is another highlight engaging the reader. The exposition is user-friendly, yet rigorous, so that a broad audience consisting of students, math teachers and instructors, computer scientists and other professionals, along with the mathematically curious will all benefit from this book.

Finally, Pell and Pell–Lucas Numbers provides enjoyment and excitement while sharpening the reader’s mathematical skills involving pattern recognition, proof-and-problem-solving techniques.

Thomas Koshy is Professor Emeritus of Mathematics at Framingham State University in Framingham, Massachusetts. In 2007, he received the Faculty of the Year Award and his publication Fibonacci and Lucas numbers with Applications won the Association of American Publishers' new book award in 2001. Professor Koshy has also authored numerous articles on a wide spectrum of topics and more than seven books, among them, Elementary Number Theory with Applications, second edition; Catalan Numbers with Applications; Triangular Arrays with Applications; and Discrete Mathematics with Applications.

Preface.- List of Symbols.- Abbreviations.- 1. Fundamentals.- 2. Pell’s Equation.- 3. Continued Fractions.- 4. Pythagorean Triples.- 5. Triangular Numbers.- 6. Square-Triangular Numbers.- 7. Pell and Pell-Lucas Numbers.- 8. Additional Pell Identities.- 9. Pascal’s Triangle and the Pell Family.- 10. Pell Sums and Products.- 11. Generating Functions for the Pell Family.- 12. Pell Walks.- 13. Pell Triangles. - 14. Pell and Pell-Lucas Polynomials.- 15. Pellonometry.- 16. Pell Tilings.- 17. Pell-Fibonacci Bridges.- 18. An Extended Pell Family.- 19. Chebyshev Polynomials.- 20. Chebyshev Tilings.- Appendix.- References.- Index.

Zusatzinfo	1 Illustrations, color; 138 Illustrations, black and white; XXIII, 431 p. 139 illus., 1 illus. in color.
Verlagsort	New York, NY
Sprache	englisch
Maße	210 x 279 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Chebyshev Polynomials • Pell Fibonacci • Pell’s Equation • Pell Triangle • Pythagorean triples • Triangular Numbers
ISBN-10	1-4614-8488-X / 146148488X
ISBN-13	978-1-4614-8488-2 / 9781461484882
Zustand	Neuware