A New Study of Expansive Mappings and Pythagorean Theorem Relationship

This paper explores the relationship between expansive mappings and Pythagoras? theorem in metric space. It examines how expansion mappings keep points apart in their images and connects this concept to the Pythagorean theorem, which deals with side length ratios in right-angled triangles. The interplay between these mappings and the theorem is analyzed to reveal geometric and topological features of metric spaces. The study highlights how expansion mappings both preserve and alter distance relationships, directly linking them to geometric principles. This paper provides a comprehensive view of geometric mapping theory through abstract principles and specific examples.