Reading: Chapter 11: pp. 201-210.
Problems: Chapter 11: 1, 2 (The cylinder is the vertical cylinder based on the unit circle in the xy-plane. As a start, try to visualize infinitely many geodesics between two different points with the same x and y coordinates.), 5, 8.
Problem O: Describe a function φ(s) measuring the angle from the x-axis to the tangent vector to the circle (parametrized by arc length) of radius r about the origin in the xy-plane. Using this description, compute the winding number (φ(2π r) - φ(0))/2π for the circle directly, without Hopf's Umlaufsatz. Assume that the circle is parametrized counterclockwise.
Last modified: (2013-04-11 02:13:29 CDT)