Aplicações do princípio de Cavalieri ao cálculo de volumes e áreas
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Data
2013-02-28
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Título de Volume
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Universidade Federal de Goiás
Resumo
In elementary mathematics teaching, it often occurs that some subjects are presented
without proper justi cation or without a coherent logical construction that makes
sense of those subjects and ideas in a wider context. The calculation of areas and
volumes is an example of a subject in which these shortcomings are usually present.
In this work, we present a model for the gradual development of the ideas involved
in the calculation of volumes, in a way that is, at once, well justi ed and approachable
by the average student at this stage. In order to achieve that, we make extensive
use of the Cavalieri Principle, which allows not only an adequate justi cation of the
expressions for the volume of cylinders, cones or spheres, but also the calculation of
volumes of other shapes, such as parts of the sphere, ellipsoids and paraboloids.
We conclude with an interesting application of the Cavalieri Principle to calculate
the area of a parabolic segment and then give a demonstration of Archimedes' theorem.
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Citação
LULA, Kariton Pereira. Aplicações do princípio de Cavalieri ao cálculo de volumes e áreas. 2013. 61 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2013.