Frenet Serret frame

I've decided to release some selected (previously unlisted) lecture videos from my calculus classes to the public. I don't plan on doing this for many videos. The main reason I'm doing this is to see how well these lecture videos appear on my cell phone, and to see how many views I get and where the videos show up in search results.
In this video, I give a quick introduction to Frenet-Serret (TNB) frames. The basic definitions are covered, including calculation of the TNB frame of a helix for all t, and of the twisted cubic for t = 0 and t = 1.
Thumbnail image created using CalcPlot3D: www.monroecc.e...
0:01 Introduction to Frenet-Serret or TNB frames
9:12 Definitions
11:27 Calculation of the TNB frame of the helix r(t) = (cos t)*i + (sin t)*j + t*k
18:56 Animation of the TNB frame for the helix
23:15 Calculation of the TNB frame of the twisted cubic r(t) = t*i + (t^2)*j + (t^3)*k for t = 0, 1
38:22 Animation of the TNB frame for the twisted cubic
40:30 Two more examples of animations of TNB frames
#SpaceCurves #FrenetSerret #TNBFrame #DifferentialGeometry

[@soumyajitpal7066]

Thank you so much sir.
I'm from India🇮🇳
This video give me a clear idea about t n b.
Thanks again for explaining clearly as well.

[@DarinBrownSJDCMath]

Glad you got something out of it!

[@Tsoi-jm5er]

I hope my professor would teach Differential Geometry like you did.

[@hellostranger2709]

Just what I needed. Thank you so much!

[@DarinBrownSJDCMath]

Glad you got something out of it!

[@BlindPomerade]

Excelent video!

[@DarinBrownSJDCMath]

Glad you liked it!

[@jacobfrancis8089]

Hi! At 15:45 for the j component, I'm confused how it turned out to be positive cosine. Kindly enlighten me.
( -sint ∙ 0 ) - (cost ∙ 1)
= 0 - cost
= -cost
Thanks in advance, sir! :D

[@DarinBrownSJDCMath]

Hi, Jacob. The reason it's cos(t) is because when you evaluate the determinant by expanding along the top row, there's the pattern of alternating signs (+, -, +) that attach to the terms. So yes, you're correct that the 2x2 determinant evaluates to -cos(t), but we pick up a factor of -1 from the expansion, and that makes it +cos(t) overall.

[@jacobfrancis8089]

@@DarinBrownSJDCMath Oooh I get it now. Thank you! ^_____^

[@marcelopau2325]

Siga así amigo, saludos desde peru