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Torsion: How curves twist in space, and the TNB or Frenet Frame

If you have a curve through space, torsion measures the degree to which the curve "twists". This is separate from how the curve "curves", which we saw was given by the curvature formula. In this video we will study the TNB or Frenet Frame given by three vectors, the Tangent, the principle Normal, and the new vector called the BiNormal vector. The Tangent and Normal Vectors define a plane and what Torsion measures is how that plane changes as you move along the curve. TYPO: Near the beginning, the Normal Vector should be 1/k dT/ds. I forgot the 1/k, where k is the curvature. **************************************************** YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems! **************************************************** ►Full Multivariable Calculus Playlist:    • Calculus III: Multivariable Calculus (Vect...   **************************************************** Other Course Playlists: ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   *************************************************** ► Want to learn math effectively? Check out my "Learning Math" Series:    • 5 Tips To Make Math Practice Problems Actu...   ►Want some cool math? Check out my "Cool Math" Series:    • Cool Math Series   ***************************************************** ►Follow me on Twitter:   / treforbazett   ***************************************************** This video was created by Dr. Trefor Bazett BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett