MATH 2700 - Euclidean and Non-Euclidean Geometry
University of Virginia, January Term 2018
Prof. David Sherman
Course description:

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.

Required materials:

-- Experiencing Geometry: Euclidean and Non-Euclidean with History (third edition), D. W. Henderson and D. Taimina
-- Flatland, E. Abbott
-- Straightedge and compass
-- Tennis ball (or equivalent) and rubber bands
-- (optional) The Thirteen Books of the Elements: Vol. 1 (Books I-II), Euclid (ed. Heath). I have in mind a Dover paperback edition which includes lots of scholarly commentary and can be had for $10-15. (The remaining 11 books of The Elements come in two separate volumes and will not be considered in the course.) Of course any text of Book I is acceptable. Since all of The Elements is available for free on the internet (and linked to the course webpage), the purchase of a book form is optional.

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