Topological Structures Between Two Closed Surfaces Inspired by An Entrance Exam Problem

We shall explore with technological tools on a problem we posed in [8], which originated from a college practice entrance question (see [3]). In this paper, we are investigating whether a certain closed surface – inspired by the aforementioned college exam problem and an a¢ ne transformation –is topologically equivalent to a sphere, utilizing the three- dimensional visualization capabilities of computer technology to aid our initial analysis. This technological a¤ordance not only makes our investigation accessible to readers with just an undergraduate mathematics background but also allows us to study this surface in detail, …nally leading us to a rigorous solution to the problem. Our work highlights the essential role that technology plays in advancing and communicating mathematical research.