TOPOLOGICAL GEOMETRY AND ITS APPLICATIONS IN MODERN ENGINEERING PROBLEMS

Abstract

Topological geometry, as a branch of mathematics concerned with properties preserved under continuous transformations, has significant applications in modern engineering, including structural analysis, robotics, material science, and network design. This study investigates the application of topological geometry principles to contemporary engineering problems, emphasizing problem-solving strategies, modeling techniques, and practical implementations. Using the IMRaD framework, the research combines literature review, computational modeling, and case studies of engineering systems where topological approaches enhance design, reliability, and efficiency. Results demonstrate that topological geometry enables robust modeling of complex structures, optimization of connectivity in networks, and innovative solutions in engineering design. The discussion addresses methodological approaches, computational challenges, and educational implications. The conclusion highlights the pivotal role of topological geometry in advancing engineering practice and fostering innovation in problem-solving strategies.