Navegando por Autor "Saavedra, Beto"

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    Experiências geoanalíticas na sala de aula
    (2019-06-29) Saavedra, Beto
    Through the solution of problems in Analytic Geometry, this work aims to discuss the potential of its concepts and formulas, which are often applied mechanically. Furthermore, it seeks to show, with due modesty, that within the teaching and learning process of this discipline there are still new horizons to be discovered and explored. This work is not intended as an introduction to Analytic Geometry, but rather as a review.
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    Geometria Analítica : rotação e translação de eixos coordenados
    (2026-04-27) Saavedra, Beto
    Rotation 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.
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    Geometria analítica: equações paramétricas do plano
    (2026-05-28) Saavedra, Beto
    This 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.