|Los Angeles Math Circle|
9/25 -- LAMC High School: Introduction to Geometry, or Is your World Flat? (Part I) -- Dr. Oleg Gleizer
In this 6-hours-long (3 meetings) mini-course, we shall compare a few 2-dimensional (2D) surfaces, the Euclidean plane, a cylinder, a Moebius plane (a.k.a. an unbounded Moebius strip), a sphere, and, if time permits, the Lobachevsky plane.
The following are well-known features of the Euclidean plane.
1. There exists one and only one straight line passing through two different points.
In the course, we shall see if these properties hold for the 2D surfaces mentioned above. Our point of view will be that of a tiny bug living on a surface. Our ultimate goal will be to see, if our world is flat (a.k.a. Euclidean). Our study will be hands-on, so please bring the tools, a few letter-size sheets, a few pencils, an eraser, a compass, and a ruler (straightedge) to every class.