The equation for the helical path length around a torus can be derived using a parameterization of the toroidal surface, specifically a torus with a cross-section radius \( r \) and a central circle radius \( R \) where \( R > r \). To find the helical path length, one must differentiate the parameterization with respect to its two parameters to obtain tangent vectors. A linear combination with undetermined coefficients is then used to create a vector field on the torus, leading to the identification of integral curves that define the helical path.
PREREQUISITESMathematicians, physicists, and engineers interested in geometric analysis, particularly those working with toroidal structures and helical paths.