Superfícies focais e pontos umbílicos Darbouxianos segundo a análise de Allvar Gullstrand
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2019-02-13
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Universidade Federal de Goiás
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Allvar Gullstrand (1862-1930) was a Swedish ophthalmologist who received the Nobel Prize in Physiology orMedicine for his studies in images and refraction of light in the eye (EHINGER; GRZYBOWSKI, 2011). For the success of his research, Gullstrand would need advanced knowledge in Physics and Geometry. In order to understand the human eye, Gullstrand (1900) studied the focal surfaces and their respective singularities using the fourth order derivatives of a surface (NORDENSON, 1962, p. 285). The main goal of this dissertation was to study Gullstrand (1904) to understand the relation between the umbilic points and focal surfaces. In this sense, there are two possibilities for the focal surfaces, say M1 and M2, which depend on the type of the Darbouxian umbilic point, being that M1 is related to the types D1, D2 or D3 and M2 to the type D3. The relation between type of Darbouxian umbilic points and the focal surface will depend on the analysis of the ridges (critical points of the principal curvatures) that pass through the respective umbilic point where, for points of type D1 or D2 passes only one ridge and through the point of type D3 passes one or three ridges.
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FERREIRA, S. C. S. Superfícies focais e pontos umbílicos Darbouxianos segundo a análise de Allvar Gullstrand. 2019. 101 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019.