An Excursion to Non-Euclidean Geometry
January 16, 2006
Bailey Hall 201
Pastries and drinks will be served at 4 pm in Bailey Hall 204
During the 19th century it became clear that Euclidean Geometry (that is geometry as we learned it in school) is not the only geometry. In the same century hyperbolic geometry and more generally differential geometry was developed. Differential geometry is a very notation-heavy subject and a lot of tools from all over the mathematical arena are needed to explain it rigorously. Rigor aside, I would like to give you a feel for some of the ideas and questions within this subject. We will start with the big question that started non-Euclidean geometry: Does the parallel postulate follow from the rest of the Euclidean postulates (axioms)? From there we will head toward my own area of research, which is a subfield of differential geometry. This talk will not give you a grand overview of non-Euclidean geometry, but hopefully you will get a feel for how exciting the subject is.
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