🎬how an orthogonal coordinate system can still have non-zero Christoffel symbols if its basis vectors

Christoffel symbols are not only about a coordinate system's basis vectors changing direction but also about them changing magnitude. While the vectors remain perpendicular, you can visually see their lengths expand or contract as you move away from the center. This change in magnitude means their derivatives are non-zero, requiring Christoffel symbols to properly describe the system. The demo proves that even an orthogonal coordinate system can have non-zero Christoffel symbols if the basis vectors vary.

The Metric Tensor Covariant Derivatives and Tensor Densities | Condensed Notesviadean on Notion