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Mathematics

Stokes' Theorem and the Unification of Vector Calculus

Quick fact

Stokes' theorem shows that every integral theorem in vector calculus—Green's theorem, the classical Stokes' theorem, and the divergence theorem—is a special case of a single, general principle that relates the integral of a derivative over a region to the integral of the original quantity over the region's boundary.

Why this is interesting

You've probably seen three separate formulas for integrating vector fields—over curves, surfaces, and volumes. But what if they're actually all the same theorem in disguise?