Distâncias astronômicas e geometria

Abstract

At every moment we have to front ourselves with some situations which make us to react about concepts, calculations and processes related to mathematical knowledge. Therefore, the theme for this work came after the Astronomy Olympic Contest, held at school, where the geography teacher expressed concern about the diculties found out by the students to solve problems which require basic knowledge in mathematics. Considering the idea that the trigonometry studies are related to applications, it is possible to explore the interdisciplinarity of this content integrating it to Astronomy, which is an area that arouses much curiosity on students. This work presents a pedagogical experience carried out in a classroom with students of a technical school, and it was developed in a reflexive way about the needs of interpreting and solving mathematically problems which involve inaccessible distances. For that it was necessary to work initially with sequenced contents: Thales Theoreme, trigonometric equations, plane geometry and spatial geometry and then present the problem with the calculation of the Earth diameter, the distance between the Earth and the Moon as well as the distance between the Earth and the Sun. Starting from this point, the students had the opportunity of overcoming some diculties they had been facing with basic mathematics and geometry used in Astronomy. Along the process, the students have presented different solutions for the comparative illustration between the astronomic distances indicated above. For illustrating the sizes of the Earth, the Moon and the Sun and their respective distances in scales, we created situations which made the students able to show creativity and reasoning capacity. For evaluating, activities with questions of the Astronomy Olympic Contest were applied in the classroom after the pedagogical experience. The results of the students were very satisfactory, once they showed a better performance in interpreting and solving problems which had been pointed out initially.