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Pellonometry

  • Thomas Koshy
Chapter

Abstract

A number of properties bridge the Pell family with trigonometry. To study them, we will frequently need to rely on an important formula in trigonometry, Euler’s formula: \(e^{ix} =\cos x + i\sin x\), where x is any real number and \(i = \sqrt{-1}\).

Keywords

Fourth Root Lucas Number Inverse Tangent Function Polynomial Family Newport News 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 38.
    P.F. Byrd, Expansion of Analytic Functions in Polynomials Associated with Fibonacci Numbers, Fibonacci Quarterly 1 (1963), 16-29.MATHMathSciNetGoogle Scholar
  2. 44.
    R.W.D. Christie, Mathematical Question, Educational Times XI (1907), 96.Google Scholar
  3. 53.
    C. Cooper and R.E. Kennedy, Problem B-742, Fibonacci Quarterly 31 (1993), 277.Google Scholar
  4. 96.
    G.C. Greubel, Solution to Problem H-666, Fibonacci Quarterly 48 (2010), 93–95.Google Scholar
  5. 97.
    G.C. Greubel, Solution to Problem H-667, Fibonacci Quarterly 48 (2010), 95.Google Scholar
  6. 126.
    T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, New York, 2001.CrossRefMATHGoogle Scholar
  7. 207.
    H.-E. Seiffert, Problem H-510, Fibonacci Quarterly 34 (1996), 187.Google Scholar
  8. 208.
    H.-E. Seiffert, Solution to Problem H-510, Fibonacci Quarterly 35 (1997), 191–192.Google Scholar
  9. 215.
    H.-E. Seiffert, Solution to Problem H-591, Fibonacci Quarterly 41 (2003), 473–475.Google Scholar
  10. 224.
    H.-E. Seiffert, Problem H-666, Fibonacci Quarterly 46 (2008), 91.Google Scholar
  11. 225.
    H.-E. Seiffert, Problem H-673, Fibonacci Quarterly 46 (2008), 283.Google Scholar
  12. 226.
    H.-E. Seiffert, Solution to Problem H-673, Fibonacci Quarterly 48 (2010), 284–286.Google Scholar
  13. 231.
    L.W. Shapiro, Solution to Problem B-742, Fibonacci Quarterly 32 (1994), 470–471.Google Scholar
  14. 266.
    D. Zeitlin, Solution to Problem H-64, Fibonacci Quarterly 5 (1967), 74–75.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Thomas Koshy
    • 1
  1. 1.Framingham State UniversityFraminghamUSA

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