Arc Length as a Parameter | Differential Geometry 3

After a long hiatus from Differential Geometry, I return to this highly-requested series as promised! The New Year is upon us and there is no better way to celebrate than with a discussion on reparametrizing with respect to arc length. In this video, I begin by discussing how reparametrizing with respect to arc length is a valid choice, and why doing this procedure is important in the context of Differential Geometry (re: unit-speed curves). I then prove two theorems related to using arc length as the parameter and the resultant unit speed properties of the curve. 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=1WWXM084fohiIqbeCwinT4bwBVTMSF9hl Patreon: https://www.patreon.com/user?u=4354534 Twitter: https://twitter.com/FacultyOfKhan #DifferentialGeometry #ArcLength #UnitSpeedCurve