The Newton Fractal’s Leonardo Sequence Study with the Google Colab

The work deals with the study of the roots of the characteristic polynomial derived from the Leonardo sequence, using the Newton fractal to perform a root search. Thus, Google Colab is used as a computational tool to facilitate this process. Initially, we conducted a study of the Leonardo sequence,...

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Bibliographic Details
Published in:International electronic journal of mathematics education 2020-05, Vol.15 (2), p.em0575
Main Authors: Alves, Francisco Regis Vieira, Machado Vieira, Renata Passos
Format: Article
Language:English
Subjects:
Coding
Collaboration
Education
Educational Technology
Equations (Mathematics)
Fractals
Mathematical Concepts
Mathematical Formulas
Mathematics
Methods
Numbers
Numerical analysis
Programming Languages
Teaching
Teaching Methods
Technology Uses in Education
Text editing
Visualization
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Summary:The work deals with the study of the roots of the characteristic polynomial derived from the Leonardo sequence, using the Newton fractal to perform a root search. Thus, Google Colab is used as a computational tool to facilitate this process. Initially, we conducted a study of the Leonardo sequence, addressing it fundamental recurrence, characteristic polynomial, and its relationship to the Fibonacci sequence. Following this study, the concept of fractal and Newton’s method is approached, so that it can then use the computational tool as a way of visualizing this technique. Finally, a code is developed in the Phyton programming language to generate Newton’s fractal, ending the research with the discussion and visual analysis of this figure. The study of this subject has been developed in the context of teacher education in Brazil.
ISSN:1306-3030
1306-3030
DOI:10.29333/iejme/6440