Variations on a Theme of Fibonacci1

Author:
Sheldon P. Gordon
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Michael B. Burns
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Volume/Issue:
Volume 116: Issue 1
Page(s):
29–47
DOI:
https://doi.org/10.5951/MTLT.2022.0120
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Subjects:
Grade(s) or Audience, Grades 9-12, Math Topic, Algebra, Sequences/Series/Patterns, Functions and Trigonometry, Algebraic Functions, Other Topic, Technology, Professional Development / Teacher Training

We introduce variations on the Fibonacci sequence such as the sequences where each term is the sum of the previous three terms, the difference of the previous two, or the product of the previous two. We consider the issue of the ratio of the successive terms in ways that reinforce key behavioral concepts of polynomials.

Supplementary Materials

    • Fibonacci Presentation 1 (4.10 MB)
    • Fibonacci Presentation 2 (3.13 MB)
    • Fibonacci Sequence and Golden Ratio (80.1 KB)
    • Fibonacci Variations (89.1 KB)
    • Fibonacci with Differences (74.9 KB)
    • Fibonacci with Product (65.4 KB)
    • Tribonacci Sequence and Ratios (82.4 KB)
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Mathematics Teacher: Learning and Teaching PK-12
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  • Lamb, E. (2016). Meet the metallic means. Scientific American, October 21.

  • Smith, Karl. (2016). The nature of modern mathematics (13th ed.). Cengage Learning.

Copyright:
© 2023 by National Council of Teachers of Mathematics, Inc.
Page Count:
19
Article Category:
Research Article
Print Publication Date:
01 Jan 2023
Online Publication Date:
Jan 2023
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