Luke Wasserman - Concrete Euclidean and Non-Euclidean Geometry, Advisor Dr. Otero

This project presents concrete models for the three classical plane geometries, Euclidean, Spherical and Hyperbolic.  It will discuss how inner products for 2- and 3-dimensional real vector spaces allow for the definition of the Euclidean and Lorentz metrics, and how coordinatizations of space provide environments in which faithful models of the three geometries can be realized.  In each of these models the identification of lines (geodesics), isometries, and the notions of parallelism are the building blocks of triangle geometry that mirror classical synthetic approaches to plane geometry.  At the end of this presentation, one, if interested, will be able to continue research of Geometry in a concrete way.