Metodos geométicos para otimização no ensino médio
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2013-07-19
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Universidade Federal de Goiás
Resumo
This present study aims to awake and to encourage teachers for a teaching methodology that promotes
more participation of the students in the Mathematics classes. This study presents Geometry
Optimization Methods and also delineates some issues in the high school environment. In the _rst part,
it presents some geometrical results in order to support solving maximum and minimum problems.
Among the geometrical tools explored in this study to minimize distances we use the Triangle Inequality
and some of its implications. In order to maximize areas we employ some characteristics of isosceles
triangles and to maximize an angle we take advantage of some properties of angles whose sides
intersect a given circle. The methods presented are, then, applied in solving many interesting
optimization problems some of which are classical. At the end of the study some additional optimization
problems are proposed in order to encourage further explorations within the context of the methods
presented in the previous sections.
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LIMA, Robison Luiz Alves de. Metodos geométicos para otimização no ensino médio. 2013. 48 f. Dissertação ( mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2013.