Publications
An overview on real division algebras
Latin American Journal of Mathematics, 2, 2
Literature review
Abstract: In this paper, I expose initial concepts of real division algebras, providing historical notes on R, C, H and O. This is done to emphasize the relevance of topological K-theory through the Bott-Milnor-Kervaire Theorem, which is at the end. For completeness, we also present some classical results about the main algebras.
Fractais: figuras de outra dimensão - parte II
Acta Legalicus, 30
Scientific dissemination
Abstract: In the second part of this study, we delve deeper into the realm of fractal figures. Our attention shifts to the intriguing concept of fractal dimension. Following that exploration, we show a practical application of this concept. Leveraging accessible technological tools like Google Earth, we unveil a method to accurately measure the length of the Brazilian coastline.
Co-author: Caio Henrique Silva de Souza.
Fractais: figuras de outra dimensão - parte I
Acta Legalicus, 29
Scientific dissemination
Abstract: In the first part of this work, we provide a detailed explanation of the concepts of algorithm and algorithmic limit. Following that, we introduce the most significant fractal figures in the history of Mathematics. These include the Cantor Set, the Koch Curve, the Koch Snowflake, the Sierpinski Triangle, and the Sierpinski Square.
Co-author: Caio Henrique Silva de Souza.
Homens de categoria
Acta Legalicus, 25
Scientific dissemination
Abstract: This paper explores fundamental concepts surrounding mathematical structures, elucidating their generality and inherent naturalness through diverse examples. I focus on the mathematical notion of a group, offering tangible instances and leveraging insights from Jean Piaget's theories on human cognition. I also expand the perspective to encompass increasingly comprehensive structures. Ultimately, the aim is to achieve an understanding of mathematical categories. In this segment, I illustrate how the previously discussed structures can be derived from the broader framework.
Uma história dos polígonos regulares
Acta Legalicus, 22
Scientific dissemination
Abstract: An intriguing challenge tackled by ancient Greek mathematicians was the task of constructing a regular heptagon using only ruler and compass. Less familiar than the problems of squaring the circle, doubling the cube, and trisecting the angle, this problem has captured our attention. In this study, we show the lone surviving ancient attempt at solving this enigma and we look into the constructibility of regular polygons using the language of Modern Mathematics. We think that drawing parallels between historical attempts and contemporary solutions offers crucial insights into the problem.
Co-author: Caio Henrique Silva de Souza.
Por que são tão complicadas algumas somas de números naturais?
Acta Legalicus, 16
Scientific dissemination
Abstract: This work treats and elementary problem: the summation of a fixed power of the initial natural numbers. In this study, we establish the presence of polynomial formulas designed for these calculations, shedding light on the intricacies of determining coefficients. By presenting and contrasting various methods, we illuminate the challenges associated with explicitly identifying these coefficients. Within the pages, the readers will find binomial coefficients, Bernoulli numbers, and the famous Vandermonde matrices.
Co-author: Caio Henrique Silva de Souza.