Pell and Pell–Lucas Numbers with Applications

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Springer, Nov 11, 2014 - Mathematics - 431 pages

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.

 

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Contents

1 Fundamentals
1
2 Pells Equation
31
3 Continued Fractions
57
4 Pythagorean Triples
79
5 Triangular Numbers
87
6 SquareTriangular Numbers
101
7 Pell and PellLucas Numbers
115
8 Additional Pell Identities
151
13 Pell Triangles
247
14 Pell and PellLucas Polynomials
255
15 Pellonometry
282
16 Pell Tilings
303
17 PellFibonacci Hybridities
325
18 An Extended Pell Family
363
19 Chebyshev Polynomials
371
20 Chebyshev Tilings
395

9 Pascals Triangle and the Pell Family
173
10 Pell Sums and Products
193
11 Generating Functions for the Pell Family
207
12 Pell Walks
227
Appendix
411
References
417
Index
423
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About the author (2014)

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.

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