Exploring Sequences through Variations on Fibonacci

Authors

  • Gordon A Swain Ashland University

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!

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.

Downloads

Published

2017-10-01

How to Cite

Swain, G. A. (2017). Exploring Sequences through Variations on Fibonacci. Ohio Journal of School Mathematics, 77(1). Retrieved from https://ohiomathjournal.org/index.php/OJSM/article/view/5923

Issue

Section

Articles