Uploaded January 2020 | Updated September 2026, 2 weeks ago

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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 youtube.com/playlist?list=PLdgVBOaXkb9DJjk8V0-RkXTnD4ZXUOFsc
Lecture Notes: drive.google.com/open?id=1WWXM084fohiIqbeCwinT4bwBVTMSF9hl
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan

#DifferentialGeometry #ArcLength #UnitSpeedCurve