Unraveling the Fibonacci, Lucas and Gibonacci sequences in GeoGebra

Authors

DOI:

https://doi.org/10.23925/2237-9657.2025.v14i1p076-094

Keywords:

Fibonacci, Lucas, Gibonacci, sequence, geometric representation

Abstract

In this work, the Fibonacci, Lucas, and Gibonacci sequences are explored from a different perspective: through geometric representations of some identities related to these sequences using the GeoGebra software and the slider tool, making the understanding of these identities more intuitive. Additionally, Cassini’s paradox is analyzed, and some applications of the Gibonacci sequences in Analytical Geometry are presented, all illustrated with GeoGebra. The geometric approach allows for a broader and more dynamic exploration, facilitating the identification of patterns and generalizations.

Author Biographies

Adriano Verdério, Universidade Tecnológica Federal do Paraná

Professor do Magistério Superior na Universidade Tecnológica Federal do Paraná (UTFPR)

Luciana da Fonseca Cruz, Secretaria de Estado da Educação do Paraná

Professora do Ensino Básico na Secretaria de Estado da Educação do Paraná (SEED-PR)

Mari Sano, Universidade Tecnológica Federal do Paraná

Professora do Magistério Superior na Universidade Tecnológica Federal do Paraná (UTFPR)

References

Benjamin, A. T., & Quinn, J. J. (2003). Proofs That Really Count: The Art of Combinatorial Proof. Washington, DC: American Mathematical Society.

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Eves, H. (2004). Introdução à história da Matemática. Campinas, SP: Editora da UNICAMP.

Grimaldi, R. P. (2012). Fibonacci and Catalan numbers: an introduction. Hoboken, NJ: John Wiley & Sons.

Horadam, A. F. (1961). A Generalized Fibonacci Sequence. The American Mathematical Monthly, 68(5), 455–459. https://doi.org/10.1080/00029890.1961.11989696

Horadam, A. F. (1962). Fibonacci Sequences and a Geometrical Paradox. Mathematics Magazine, 35(1), 1–11. https://doi.org/10.1080/0025570X.1962.11975283

Jaiswal, D. V. (1969). On Determinants Involving Generalized Fibonacci Numbers. The Fibonacci Quarterly, 7(3), 319–330. https://doi.org/10.1080/00150517.1969.12431161

Koshy, T. (2017). Fibonacci and Lucas numbers with applications, (v. 1, 2. ed). Hoboken, NJ: John Wiley & Sons.

Sigler, L. (2003). Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation. New York, NY: Springer-Verlag.

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Published

2025-06-08

How to Cite

Kitani, P. M., Verdério, A., Cruz, L. da F., & Sano, M. (2025). Unraveling the Fibonacci, Lucas and Gibonacci sequences in GeoGebra. Journal of the GeoGebra International Institute of São Paulo, 14(1), 076–094. https://doi.org/10.23925/2237-9657.2025.v14i1p076-094

Issue

Vol. 14 No. 1 (2025)

Section

Artigos

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Copyright (c) 2025 Journal of the GeoGebra International Institute of São Paulo

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