Euclidean and Non-Euclidean Geometry

(1.5-3 Credit Hours) · Undergraduate

justify with reasoned logical argument basic properties of triangles, circles and polygons in the Euclidean plane; describe measures of curvature, both extrinsic and intrinsic, applicable to smooth surfaces in three-dimensional Euclidean space; identify, and justify with reasoned logical argument, significant geometric features and properties of the hyperbolic plane, and the corresponding features and properties of the disk that represent them in the Poincare disk model of the hyperbolic plane. Oxford Students will be familiar with the idea of projective space and the linear geometry associated to it, including examples of duality and applications to Diophantine equations.