JUA - CPROD - Recursos educacionais
URI Permanente para esta coleçãohttps://repositorio.univasf.edu.br/handle/123456789/692
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Item Uma demonstração matricial do Teorema de König (sem o uso de grafos)(2026-11-05) Saavedra, Beto; Kuzimoto, DiegoThis work presents a matrix-based proof of König’s Theorem without relying on graph theory, taking as its starting point the mathematical foundations of the Hungarian Method for solving optimal assignment problems. Initially, the concepts of cost matrix, optimal assignment, and equivalence between matrices are introduced, accompanied by an application illustrating the main steps of the algorithm. Subsequently, the termination of the procedure and the determination of optimal solutions are discussed. The proof of König’s Theorem is developed through a matrix-based approach, using auxiliary notation and a result referred to as **Diego’s Lemma**. This text was prepared as supporting material for the short course **MC55 – A Matrix-Based Proof of König’s Theorem Without Using Graph Theory**, delivered during the **12th Biennial Meeting of the Brazilian Mathematical Society**, held at the Federal University of Rio Grande do Norte (UFRN), in Natal, Brazil, from August 3 to 7, 2026, with a total duration of four hours. The presentation aims to provide an alternative perspective on understanding König’s Theorem and its relationship with the Hungarian Method, emphasizing elementary matrix-based arguments.Item Geometria analítica: equações paramétricas do plano(2026-05-28) Saavedra, BetoThis material presents, in a visual and educational way, the idea of a plane in parametric form in Analytic Geometry. The plane is defined by an initial point (P_0) and by two non-parallel direction vectors, (\vec a) and (\vec b). From the equation (P = P_0 + s\vec a + t\vec b), it is shown that, as the parameters (s) and (t) vary, the points belonging to the plane are generated. Thus, the animation helps students understand how the direction vectors determine the orientation of the plane in space.Item Geometria Analítica : rotação e translação de eixos coordenados(2026-04-27) Saavedra, BetoRotation and translation of coordinate axes are fundamental techniques in Analytic Geometry used to simplify equations. The equation xy-x+y-3=0 represents a hyperbola. The mixed term (xy) indicates that the curve is not aligned with the original coordinate axes. For this reason, we apply a rotation of the axes by an angle (\theta) in order to eliminate the mixed term and obtain a simpler form of the equation. After the rotation, a translation of the axes may also be performed, shifting the origin to the center of the curve. In this way, the canonical form of the hyperbola is obtained. The change of coordinates makes it possible to: * identify the type of conic; * find the center of the curve; * determine symmetries; * facilitate the calculation of geometric elements such as vertices, foci, and asymptotes. The video allows us to visualize dynamically the harmony between the rotated axes (x_1) and (y_1), the angle (\theta), and the equations representing the hyperbola throughout the geometric transformation.Item Equação Canonica da Elipse(2026-04-09) Beto, Saavedra> Playful educational material on the canonical equation of the ellipse, developed to support learning in Analytic Geometry through visual and intuitive explanations.