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: https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/ 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