Closed Curves and Periodic Curves | Differential Geometry 4

This video is a continuation of my series on Differential Geometry, and is a discussion about closed and periodic curves. In this video, I begin by discussing the difference between open and closed curves. I then move on to define important terms, such as a periodic curve, a closed curve, and the period of the curve. I then prove an important theorem that if a smooth regular curve is periodic, then its unit-speed reparameterization (i.e. reparameterization with respect to arc length per the previous video) is also periodic. Questions/requests? Let me know in the comments! Pre-reqs: the previous videos in my playlist https://www.youtube.com/playlist?list=PLdgVBOaXkb9DJjk8V0-RkXTnD4ZXUOFsc Lecture Notes: https://drive.google.com/open?id=1JZjgA997IVsqrTmYK4R4hjAhQl1UJ6KN Patreon: https://www.patreon.com/user?u=4354534 Twitter: https://twitter.com/FacultyOfKhan #DifferentialGeometry #ArcLength #PeriodicCurve