Visualizing the Newtons Fractal from the Recurring Linear Sequence with Google Colab: An Example of Brazil X Portugal Research

Francisco Regis Vieira Alves; Renata Passos Machado Vieira; Paula Maria Machado Cruz Catarino

doi:10.29333/iejme/8280

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Francisco Regis Vieira Alves ¹ ^* , Renata Passos Machado Vieira ², Paula Maria Machado Cruz Catarino ³

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¹ Federal Institute of Science and Technology of Ceara, BRAZIL² Federal Institute of Education, Science and Technology, Fortaleza, BRAZIL³ UTAD - University of Trás-os-Montes and Alto Douro, PORTUGAL^* Corresponding Author

Abstract

In this work, recurrent and linear sequences are studied, exploring the teaching of these numbers with the aid of a computational resource, known as Google Colab. Initially, a brief historical exploration inherent to these sequences is carried out, as well as the construction of the characteristic equation of each one. Thus, their respective roots will be investigated and analyzed, through fractal theory based on Newton's method. For that, Google Colab is used as a technological tool, collaborating to teach Fibonacci, Lucas, Mersenne, Oresme, Jacobsthal, Pell, Leonardo, Padovan, Perrin and Narayana sequences in Brazil and Portugal. It is also possible to notice the similarity of some of these sequences, in addition to relating them with some figures present and their corresponding visualization.

Keywords

teaching
characteristic equation
fractal
Google Colab
Newton's method
sequences

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 15, Issue 3, October 2020, Article No: em0594

https://doi.org/10.29333/iejme/8280

Publication date: 17 May 2020

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How to cite this article

APA

Alves, F. R. V., Machado Vieira, R. P., & Cruz Catarino, P. M. M. (2020). Visualizing the Newtons Fractal from the Recurring Linear Sequence with Google Colab: An Example of Brazil X Portugal Research. International Electronic Journal of Mathematics Education, 15(3), em0594. https://doi.org/10.29333/iejme/8280

Vancouver

Alves FRV, Machado Vieira RP, Cruz Catarino PMM. Visualizing the Newtons Fractal from the Recurring Linear Sequence with Google Colab: An Example of Brazil X Portugal Research. INT ELECT J MATH ED. 2020;15(3):em0594. https://doi.org/10.29333/iejme/8280

AMA

Alves FRV, Machado Vieira RP, Cruz Catarino PMM. Visualizing the Newtons Fractal from the Recurring Linear Sequence with Google Colab: An Example of Brazil X Portugal Research. INT ELECT J MATH ED. 2020;15(3), em0594. https://doi.org/10.29333/iejme/8280

Chicago

Alves, Francisco Regis Vieira, Renata Passos Machado Vieira, and Paula Maria Machado Cruz Catarino. "Visualizing the Newtons Fractal from the Recurring Linear Sequence with Google Colab: An Example of Brazil X Portugal Research". International Electronic Journal of Mathematics Education 2020 15 no. 3 (2020): em0594. https://doi.org/10.29333/iejme/8280

Harvard

Alves, F. R. V., Machado Vieira, R. P., and Cruz Catarino, P. M. M. (2020). Visualizing the Newtons Fractal from the Recurring Linear Sequence with Google Colab: An Example of Brazil X Portugal Research. International Electronic Journal of Mathematics Education, 15(3), em0594. https://doi.org/10.29333/iejme/8280

MLA

Alves, Francisco Regis Vieira et al. "Visualizing the Newtons Fractal from the Recurring Linear Sequence with Google Colab: An Example of Brazil X Portugal Research". International Electronic Journal of Mathematics Education, vol. 15, no. 3, 2020, em0594. https://doi.org/10.29333/iejme/8280