A Simple yet Powerful Math Trick

Video Description

Join my new Patreon community: https://www.patreon.com/abidebyreason . You'll get access to additional content, help shape final edits, and get early access to new videos. An equally valuable way to support ABR is to just share these videos with others. Thank you! There is an interesting duality between points and lines. A duality that also occurs between fundamental quantities found in both classical mechanics and thermodynamics. By the end of this video you will see that all these dualities are really just basic applications of one simple, yet powerful math trick known as the Legendre Transform. _____ Sources: Making Sense of the Legendre Transform by Zia et al Legendre Transform for Dummies by Carl E. Mungan A Graphical Derivation of the Legendre Transform by Sam Kennerly Amazing lecture covering similar topics: https://www.youtube.com/watch?v=GOkZs2RZMQY&list=PL5E4E56893588CBA8&index=10&t=1194s Nice, short clip of above lecture on the Legendre Transform: https://www.youtube.com/watch?v=x2WXtvVtrUA&t=66s _____ Typo: at 14:55 "dU is at a minimum" should be written "U is at a minimum", "dF is at a minimum" should be written "F is at a minimum", and so on _____ Music: Epidemic Sound Animations created using Manim: https://www.manim.community/ Illustrations and Thumbnails: Christine Kosakowski