Exploring Sequences through Variations on Fibonacci

Gordon A Swain

Abstract


Leonardo Pisano’s word problem, which led to the ubiquitous Fibonacci sequence, provides a point of departure for several explorations. The variations are motivated by more realistic assumptions to the original rabbit problem. Through these activities, students practice data generation, pattern-finding, developing formal proofs, carrying out generalizations, and data analysis. And they might even have some fun!

Full Text:

PDF

References


Alfred, B. U. (1963). Exploring Fibonacci numbers. Fibonacci Quarterly, 1(1), 57-62.

Burger, E. B., Chard, D. J., Hall, E. J., Kennedy, P. A., Leinwand, S. J., Renfro, F. R., Seymour, D. G., & Waits, B. K. (2007). Holt algebra 2. Orlando, FL: Holt, Rinehart and Winston.

Burger, E. B., Chard, D. J., Kennedy, P. A., Leinwand, S. J., Renfro, F. R., Roby, T. W., & Waits, B. K. (2011). Holt McDougal algebra 1. Orlando, FL: Houghton Mifflin Harcourt Publishing Company.

Chapin, S. H., Illingworth, M., Landau, M. S., Masingila, J. O., & McCracken, L. (2001). Middle grades math tools for success: Course 3 Preparing for algebra and geometry. New Jersey: Prentice-Hall.

Hoggatt, V. E. & Lind, D. A. (1969). The dying rabbit problem, Fibonacci Quarterly, 7(5), 482-487.

O’Conner, J. J. & Robertson, E. F. (1998). Leonardo Pisano Fibonacci, MacTutor History of Mathematics archive. Retrieved from http://www-history.mcs.st-andrews.ac.uk/Biographies/Fibonacci.html

Oller-Marcén, A. M. (2009). The dying rabbit problem revisited, Integers, 9(1), 129-138.

Pisano, L. (2002), Liber abaci (L. E. Sigler, Trans.). New York: Springer.

Stewart, J., Redlin, L., & Watson, S. (2012). Precalculus: Mathematics for calculus (6th ed.). Belmont, CA: Brooks/Cole, Cengage Learning.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Gordon A Swain

The Ohio Journal of School Mathematics is published by the Ohio Council of Teachers of Mathematics and hosted by The Ohio State University Libraries.

If you encounter problems with the site or have comments to offer, including any access difficulty due to incompatibility with adaptive technology, please contact libkbhelp@lists.osu.edu.

ISSN 2472-5986 (print)
ISSN 2472-601X (online)