Nosso principal objetivo neste trabalho é a determinação de regiões de segurança em balística. Por região de segurança entendemos a região do espaço tridimensional que fica livre da ação de projéteis. A determinação da região de segurança será reduzida ao cálculo da envoltória de uma família de trajetórias, indexada segundo o ângulo de tiro.
An initiation to scientific research project was proposed for two undergraduate students in Environmental Engineering, with the porpuse of studing a generalization of the hypotrochoid and epitrochoid curves. The GeoGebra software is the facilitator of the team of two professors and the students. The difficulties of the mathematical proofs become, in the environment of the dynamic geometry, exercises of construction of curves that, arranged in sequence, determined the generalization of the well-known hypotrochoid curve, result that is the detailed in this work. From this first discovery, the transition to epitrochoid curves or more general curve,s becomes an iterative application and an applicattion of mathematical induction. This study has demonstrated the importance of the computational tool, specially for its contribution in the visualization of theoretical results as well as for its simplicity in coding.
A mathematical modeling project was proposed for a student of a Distance Education in a Mathematics Degree course, which involved the use of solids of revolution. In this paper, we present and analyze the teaching-learning process for the development of modeling in this experience, based on the communication established between student and teacher. In order to facilitate student’s self-learning, the GeoGebra software was chosen as an aid tool in computational implementation. In the teaching proposal, the student was asked to identify a building that had the shape of a figure of revolution and the Cathedral of Brasilia, located in the city of Brasilia, Brazil, was chosen, after verifying the feasibility for completion of this model in the GeoGebra environment. The analysis of the dialogues between student and researcher shows that the interaction was based on Prado and Valente's approach of “being virtually together” and that the process of the mathematical modeling took place in gradual steps, helping to meet the mathematical and coding needs. We conclude that GeoGebra proved to be a powerful software program, which improves the visualization of the rotation motion of the desired solid generating curve and facilitated the necessary adjustments in the parameters of the algebraic expression of the curve. Thus, this experience shows that it is possible for the teacher to work the solids of revolution from a real situation, which mobilized the student for meaningful learning.
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