The discussion centers on the asymmetry between Stokes' theorem and Gauss' theorem in calculus. Stokes' theorem relates a closed line integral to surface integrals on any arbitrary surface bounded by the same curve, while Gauss' theorem connects a closed surface integral to the volume integral within a unique volume bounded by the same surface. The asymmetry arises from the dimensional differences, where a closed curve can enclose multiple surfaces, but a closed surface defines a unique volume. The conversation highlights the importance of topology in understanding these concepts.
PREREQUISITESMathematicians, physicists, and engineering students interested in vector calculus, particularly those exploring the implications of Stokes' and Gauss' theorems in higher dimensions.
@feynman1 You apparently got your answer. If you still have problems, then we may have communication problems, which is not unlikely since we are restricted to verbal only communication.PeroK said:Also, this is the third post on the subject. It was already answered in the threads mentioned in post #12 above. Here, for example, is a good answer to the question:
https://www.physicsforums.com/threa...d-by-the-same-curve-in-stokes-theorem.989709/