Orientable vs Non-Orientable Surfaces and the Mobius Strip

One property that a surface may or may not have is orientability. Loosely, this means it has two distinct sides. For example the surface of a sphere has an inside and an outside, but a Mobius Band only has one side. More specifically, a surface is orientable if we can continuously assign a field of normal vectors, which is like choosing one of the two sides. This is going to be useful for us in Vector Calculus as we will be talking about the flux across a surface from one side to the other, and so we will want to restrict to be talking about orientable surfaces.

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[Mrbananaice]

My Calc 3 exam average was 65 after my first two exams. Then I started watching your videos and I got a 93 on my third exam and I’m confident for the final. Thank you for the content.

[xoxoxoxoxoxoxo]

this channel is literally a hidden gem

[ammararashid]

This is really a hidden diamond!
Thank you so much sir for this beautiful 3D visualization. I got this video randomly and now I decided to watch all the videos related to my topic now :)

[JamesChangViolin]

Great video! We watched it during Multivariable class.

[willowsmith]

This channel has helped me enjoy calculus so much!! thank you!! The quality is amazing and your explanations so clear!

[QuocDatPhung]

Subscribed! I have Discrete Math and Linear Algebra next semester and I'm desperately trying to learn them in advance. Thank you for your content! You are one of the people who inspired me to start a Youtube channel make math videos too!

[swarajyalaxmi]

i have seen every single video in this playlist, amazing explation

[beyzaatasever]

your approach to math feels safe haha thank you !!

[Jewelsonn]

There are two sides obviously. The other side's dimensions are paper thin. That's why we cannot see the whole mobius strip. Why is this hard to grapse? Too distracted to see the lines drawn on one side?

[PiniiXever]

the person who disliked failed this course

[JoseRamirez-ptrn]

Hope you are well. I wanted to know, could you help me find cases of non-orientable surfaces other than morbius tape?

[raviphanindra]

thanks a lot for your clear explanation.

[cantorbernoulli]

BIg thanks dr.trefor for everything ( i pass differential equations cause of you...hope calc4 too ), hope one day i am able to return you your offer.

[kimbalcalkins]

Would a polarized mobius strip change polarization when traversed ?

[kaiyin]

but what if you rotate the mobius strip twice instead of once? you get 2 sides

[korky-]

Signed,
Sincerely yours_
(From a person this been reading much on the fascinating, ongoings at this place and its numerous
Physical science affiliated implications!)
Korky=
Carl Aserio
Yonkers NY .

[humann]

"non-manifold" and "non-orientable" are not interchangeable terms or are they?

[chandrakantpandey]

Sir,
 In R2, we have two different types of line integrals, the tangential line integral
∫F⋅dr
and the normal line integral
∫F⋅nds.

However, for all the surface integral, I have only seen the normal surface integral defined by
∬F⋅ndS
is there a similar concept that is close to the tangential line integral ∫F⋅dr?

[tahamr]

Thank you such amazing content Dr. Trefort Bazett. What tools you use in your videos for your 3D graphs? Any other tools you recommend? Preferably that are free and open source. Thank you once again.

[placeholdername]

Here after the "Why did the chicken cross the mobius strip" joke