Geometric Intuition Behind the Inverse Function Theorem and Legendre Transformation
2025-05-05
This article provides a geometrically intuitive explanation of the inverse function theorem and Legendre transformation. Avoiding dry formula derivations, the author uses visual methods like graph transformations and reflections to illuminate the relationship between the derivative of an inverse function and its original function, and how the Legendre transformation solves integrals of inverse functions. Using arctan x as an example, the article clearly explains the application of these important mathematical tools, highlighting their broad use in fields like physics.