https://ri.ufs.br/jspui/handle/riufs/2568 2026-08-09T15:46:05Z 2026-08-09T15:46:05Z Santos, Gabriel dos https://ri.ufs.br/jspui/handle/riufs/25757 2026-08-07T13:53:40Z 2026-07-10T00:00:00Z

Título: Uma introdução histórica à geometria hiperbólica e aplicações trigonométricas Autor(es): Santos, Gabriel dos Abstract: This work analyzes the historical and mathematical evolution of geometry, focu-sing on the rupture of the Euclidean dogma and the consolidation of hyperbolic geometry as a foundation for modern physics. The research aims to describe the transition from Euclid’s axiomatic system to non-Euclidean models, demonstrating how the negation of the fifth postulate grounds new understandings of space. The method utilizes a bibliographic and documental review of a deductive nature, based principaly in Barbosa’s works to reconstruct the logical rigor of geometric demonstrations(BARBOSA, 2007). The discussion covers the failed attempts by mathematicians such as Ptolemy, Proclus, and Saccheri to prove the parallel postu-late, culminating in the independent discovery by Gauss, Bolyai, and Lobachevsky. The text details elementary properties of neutral and hyperbolic geometry, suchas Saccheri and Lambert quadrilaterals, generalized triangles, and hyperbolic tri-gonometry. The results highlight that hyperbolic geometry provides the necessarymathematical framework for Einstein’s Theory of Relativity.

2026-07-10T00:00:00Z Santos, Beatriz Oliveira https://ri.ufs.br/jspui/handle/riufs/25672 2026-07-27T11:01:10Z 2026-07-13T00:00:00Z

Título: O jogo cashflow, adaptado ao scratch, como ferramenta pedagógica para o ensino de educação financeira Autor(es): Santos, Beatriz Oliveira Abstract: This study investigates the potential of the game Cashflow, adapted for the Scratch platform, as a pedagogical tool for teaching Financial Education. Given the complexity of the current economic scenario and the guidelines of the National Common Curricular Base (BNCC), the research seeks to answer how the use of this digital tool contributes to the development of financial skills. Methodologically, the study adopts a mixed-methods approach and is grounded in Didactic Engineering, structured into the phases of preliminary analysis, a priori analysis, experimentation, and a posteriori analysis. In this context, the analysis of interactions was based on the Theory of Didactic Situations (TDS), following the phases of action, formulation, validation, and institutionalization. Furthermore, the experiments were conducted with undergraduate students in Mathematics and 3rd-year high school students. Thus, the results demonstrate that the game promotes collaborative teaching and the active construction of knowledge, allowing the simulation of real-life situations such as cash flow management, decision-making, and investment analysis. Moreover, the mobilization of BNCC skills related to percentage and interest calculations was observed.

2026-07-13T00:00:00Z Silva, Rafael Fagundes Bitencourt https://ri.ufs.br/jspui/handle/riufs/24859 2026-03-31T13:41:35Z 2026-03-04T00:00:00Z

Título: O número de classes de um corpo de números Autor(es): Silva, Rafael Fagundes Bitencourt Abstract: This monograph aims to address the structure of number fields and their ring of integers, focusing on the class group. More specifically, it aims to study its order, proceeding from the algebraic basis to analytical constructions. As applications of the theory, we study the class group of two types of fields, which are essential to Algebraic Number Theory: the cyclotomic fields and quadratic fields.

2026-03-04T00:00:00Z Lopes, Igor de Santana https://ri.ufs.br/jspui/handle/riufs/24841 2026-03-24T23:38:57Z 2026-02-13T00:00:00Z

Título: Sizígias de um Módulo Autor(es): Lopes, Igor de Santana Abstract: This work aims to analyze the syzygies of a module over a commutative ring, emphasizing the structure and properties of the syzygies module. Starting from the definition and characterization of nontrivial linear relations between generators, we demonstrate how these structures allow us to measure the distance of a module from the condition of being free. The research includes the study of the properties and behavior of syzygies, as well as their implications for understanding modular structures in the context of commutative algebra. Examples are presented to illustrate and substantiate the theoretical results, thus providing a clear approach to the topic.

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