University of Virginia, January Term 2018

Prof. David Sherman

Euclid's *Elements* was the standard reference in geometry for about 2,000 years. In this course we will examine the assumptions and methods in the original text of Book I, then see how both of these have evolved over the last 200 years. Apart from Euclid, the main topics include the following: symmetries, spherical geometry, curvature, the dissection theory of area, constructible numbers, and the discovery of non-Euclidean geometry. Mathematical concepts will not always be presented in their most general and technical form, but there will be at least enough detail to facilitate simple computations.

Students will be challenged to think critically, to make conjectures, and to compose rigorous arguments. For geometries other than the plane, we will use various physical models: rubber bands on spheres, strings wrapped around cylinders, paper approximations to the hyperbolic plane, etc. Significant class time will be devoted to experimentation and group work on problem sets.

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-- Straightedge and compass

-- Tennis ball (or equivalent) and rubber bands

-- (optional)

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