The Cyclic Identity for Partial Derivatives: Unraveling the Mystery of -1
2024-12-16
This article explores the cyclic identity for partial derivatives: ∂z/∂x * ∂x/∂y * ∂y/∂z = -1, rather than the intuitive 1. Through examples and various proof methods, including differential forms and geometric interpretations, the article reveals the mathematical principles behind this seemingly counterintuitive identity. The author also discusses its applications in physics and offers intuitive explanations.