Journal article Open Formalizing Mechanical Analysis Using Sweeping Net Methods II: Written Without Complex Analysis and With Complex Analysis

Published with great thanksgiving for Yaohushua, the living One Yahowah, "Jesus Christ." In previous work, Formalizing Mechanical Analysis Using Sweeping Net Methods I, sweeping net methods have been extended to complex analysis, relying on the argument of complex functions defined on the unit circle. In this paper, we reformulate these methods purely within a real-valued and geometric framework, avoiding the use of complex analysis. By redefining the sweeping net constructs and the associated theorems using real functions and geometric interpretations on the unit circle, we demonstrate how singularities and their approximations can be effectively analyzed without the need for imaginary numbers. This approach provides intuitive geometric insights and broadens the applicability of sweeping net methods in mathematical analysis.