https://repositorio.ufu.br/handle/123456789/5155 Fri, 11 Sep 2026 18:58:13 GMT 2026-09-11T18:58:13Z https://repositorio.ufu.br:443/retrieve/3d344d47-9a9e-4588-b62f-969a9f400189/IME-removebg-preview.png https://repositorio.ufu.br/handle/123456789/5155 https://repositorio.ufu.br/handle/123456789/50178 Title: Sobre as singularidades de contatos de superfícies genéricas em R^3 Abstract: In this work, we investigate the differential geometry of a smooth surface M immersed in R^3 through the study of its contact with planes, spheres, and lines from the singularity theory viewpoint. Each type of contact is described by the singularities of three associated families of functions: the family of height functions, the family of distance squared functions, and the family of orthogonal projections, respectively. We show that R- (or A-) singularities of these families determine special points and curves on the surface, called robust features. We present the characterization and description of the parabolic curve, the flecnodal curve, the ridge curve, and the cusp of Gauss. In particular, we show that the parabolic curve and the flecnodal curve have second-order contact at the cusp of Gauss. Finally, by analyzing the apparent contour of the surface, we establish an alternative proof of Koenderink’s Theorem. Fri, 27 Feb 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/50178 2026-02-27T00:00:00Z https://repositorio.ufu.br/handle/123456789/50109 Title: Efeito de diferentes dosagens do adubo orgânico à base de casca de maracujá na cultura da mandioca no Cerrado Wed, 04 Mar 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/50109 2026-03-04T00:00:00Z https://repositorio.ufu.br/handle/123456789/49996 Title: “E agora, cinco?”: uma história virtual do conceito para o ensino da tangente no ensino médio Abstract: This study aims to analyze the contributions of an intentional organization of teaching, grounded in the Logical-Historical Movement and the Guiding Teaching Activity, to the appropriation of the concept of tangent by high school students. It is based on the understanding that Mathematics teaching should provide students with access to the historical conditions that gave rise to concepts, fostering the development of theoretical thinking. The research is characterized as qualitative and was developed through the elaboration and implementation of a Learning Triggering Situation (LTS), which addressed historical elements related to the emergence of the concept of tangent. The activity was organized to engage students through a Virtual History of the Concept, designed to highlight the need for the concept of tangent and enable the investigation of its conceptual nexuses. For the analysis of the empirical material, two analytical axes were established: the understanding of the historical necessity of the concept of tangent and the identification of the conceptual nexuses and students' appropriation of this concept. The results of this research indicate that the articulation between the study of the Logical-Historical Movement of concepts and the organization of teaching through the Guiding Teaching Activity constitutes a powerful approach to the teaching of trigonometry in the school context, insofar as it enables students to approach the conditions that gave rise to mathematical concepts and fosters an understanding of the conceptual relationships that structure them. Fri, 20 Mar 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/49996 2026-03-20T00:00:00Z https://repositorio.ufu.br/handle/123456789/49994 Title: Construção de bases de Gröbner para ideais polinomiais sobre um corpo K Abstract: This work presents an introduction to the theory of Gröbner bases for polynomial ideals in the ring K[x1,...,xn] over an arbitrary field K. The aim of this work is to develop the main foundations of this theory, establishing the results necessary for the construction and characterization of Gröbner bases. To this end, it adopts a theoretical approach, in which the concepts, definitions, and proofs are developed progressively. Initially, it presents fundamental results on ring theory, monomial orderings, and the division algorithm in several indeterminates, extending to the multivariate case tools previously available only for polynomials in one indeterminate. Next, it characterizes monomial ideals and proves Dickson's Lemma and Hilbert's Basis Theorem, from which the existence of Gröbner bases for every polynomial ideal follows. Subsequently, it establishes Buchberger's Criterion and Buchberger's Algorithm, culminating in the characterization of minimal and reduced Gröbner bases. The results developed make it evident that Gröbner bases provide effective methods for solving problems involving polynomial ideals and can serve as a foundation for the future study of applications of the theory. Tue, 04 Aug 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/49994 2026-08-04T00:00:00Z