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Karl Micael von Delwig: Ellipser från Apollonius till Newton

Bachelor thesis

Time: Fri 2023-06-09 09.30

Location: Meetingroom 41

Respondent: Karl Micael von Delwig

Supervisor: Torbjörn Tambour

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In this work you will be able to follow the history of the ellipse from antiquity to the beginning of the 18th century. When Apollonius gave the ellipse its name in the 2nd century BC, he found no application for his geometric figure. Over time, mathematicians came to discover that the ellipse was more interesting than they initially thought. When Rene Descartes introduced a rectangular coordinate system in the 17th century and was able to transform the ellipse from a geometric object into an algebraic object, it turned out that the ellipse and other conic sections correspond to curves given by quadratic equations. In the 17th century, Johannes Kepler was able to show, based on Tycho Brahe's astronomical measurement data, that the planetary orbits were ellipses with the sun at one focal point. After that, Isaac Newton was able to calculate the forces between the celestial bodies based on the fact that the planetary orbits were ellipses and arrive at the modern law of gravitation. This is certainly not a bad contribution of a geometric figure that was initially thought to lack important applications. In this work, I do not claim to have covered everything about the historical development of the ellipse, but I still hope to have covered the most important parts of the mathematical history of the ellipse.