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!

#DifferentialGeometry #ArcLength #PeriodicCurve

[ilmbrk]

This channel is a true gem. I am so happy that aside from “simple“ math channels like numberphile or standupmaths this type of in depth math content exists. Keep it up!

[nakulghate]

I got to confess - I am not a math student, took Differential geometry of curves and surfaces to pass my time during the quarantine and was studying from the book by Carmo, Manfredo. The book is thorough in explanation but not being a math major, I am having some difficulty understanding it. The way you are explaining it is hands down one of the best. The lectures really got me interested in it even more. This channel surely needs a lot of recognition. Thank you.

[TheBeautyofMath]

Ok I figured out how to add featured channels to my YouTube channels page. You are now one of two featured channels on my page. Hopefully my students/subscribers find it and are able to see this amazing channel. Your extensive knowledge and teaching quality for high level math will be a great resource for all college students.

[michaeljburt]

Absolutely fantastic. Extremely well explained, and you arent skipping over the derivation/assumption details which imo is so important.

[gonzalezm]

You’re the best! Thank you for continuing differential geometry 😁

[ynsszr]

i know its too much :((( but, could you please upload MORE of these kind of videos. these topics in math and physics are the hardest ones to understand and %95 of schoold teachers either does now how to explain or just doesnt care.. if was rich like bill gates, i would gladly give half of my money to you and the people like you on youtube... this is how good you are at explaining the thing which are hard to explain...
THANK YOU!!!
i wish you best in your life..

[duckymomo]

U know even when I write gamma, it looks like r(t) and I keep thinking it’s r(t)

γ(t)

[riveredge]

Reparameterization doesn't change the shape of the curve. It only changes the representation method. Closed curve is closed curve no matter how it is parameterized.

[mikevaldez]

Wow, amazing comment from yunus; however, I am inclined to believe if he had Bill Gate's money he wouldn't be on this site😂

[lakshmirajagopalan]

The closed-ness property is not invariant under reparameterization?

[goldengeek]

Do you get your content from anywhere particular? Like a textbook or a website or something else. These videos are great and all but I'm always left wanting more.

[icodegurumoderator]

is Sine/Cosine curve a closed function? It is periodic