Ellipses of Apollonius, Newton, and Dandelin
Date Issued
2015
Date
2015
Author(s)
Shen, Yi-Ting
Abstract
This thesis consists of three chapters. In chapter one, we review the work of conic sections by Greek mathematician Apollonius, and the theorem on conjugate diameters of ellipse. In chapter two, we explain Newton’s proof of “the centripetal force is inversely proportional to the square of distance”. In the proof, the above mentioned theorem on conjugate diameters played an important role. In chapter three, we introduce the conic modeling by Dandelin, a Belgian mathematician, which shows the geometrical meaning of the focus and the directrix of ellipse. We then calculate the eccentricity of conic sections by Dandelin’s modeling and classify the locus of the sundial shadow.
Subjects
conic section
ellipse
Apollonius
Newton
Dandelin
Type
thesis
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