The decimal string of the golden ratio

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 1, Pages 27—31
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Authors and affiliations

J. V. Leyendekkers
Faculty of Science, The University of Sydney
NSW 2006, Australia

A. G. Shannon
Faculty of Engineering & IT, University of Technology
Sydney, NSW 2007, Australia

Abstract

The decimal expansion of the Golden Ratio is examined through the use of various properties of the Fibonacci numbers and some exponential functions.

Keywords

  • Fibonacci sequence
  • Lucas sequence
  • Golden Ratio

AMS Classification

  • 11B39
  • 11B50

References

  1. Atanassov, K., V. Atanassova, A. Shannon, J. Turner. New Visual Perspectives on the Fibonacci Numbers. New York: World Scientific, 2002.
  2. Carlitz, L. A binomial Identity Arising from a Sorting Problem, SIAM Review. Vol. 6, 1964, 20–30.
  3. Gougenbaum, A. About the Linear Sequence of Integers and that Each Term is the Sum of the Two Preceding. The Fibonacci Quarterly. Vol. 9, 1971, 277–295, 298.
  4. Havil, J. The Irrationals: A Story of the Numbers You Can’t Count on. Princeton & Oxford: Princeton University Press, 2012.
  5. Hoggatt, V. E., Jr. Fibonacci and Lucas Numbers. Boston: Houghton-Mifflin, 1969.
  6. Leyendekkers, J. V., A. G. Shannon. 2012. On the Golden Ratio (submitted).
  7. Livio, M. The Golden Ratio. New York: Golden Books, 2002.
  8. Shannon, A.G. Some Lacunary Recurrence Relations. The Fibonacci Quarterly. Vol. 18, 1980, 73–79.
  9. Shannon, A.G., J.V. Leyendekkers. Pythagorean Fibonacci Patterns. International Journal of Mathematical Education in Science and Technology. Vol. 43, 2012, 554–559.

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Cite this paper

APA

Leyendekkers, J., & Shannon, A. (2014). The decimal string of the golden ratio. Notes on Number Theory and Discrete Mathematics, 20(1), 27-31.

Chicago

Leyendekkers, JV, and AG Shannon. “The Decimal String of the Golden Ratio.” Notes on Number Theory and Discrete Mathematics 20, no. 1 (2014): 27-31.

MLA

Leyendekkers, JV, and AG Shannon. “The Decimal String of the Golden Ratio.” Notes on Number Theory and Discrete Mathematics 20.1 (2014): 27-31. Print.

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