Classroom Experiences in Introducing Students to Conjectures, Exploration and Visual Proofs Using Experiments on the Möbius Strip

摘要

Abstract We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the Möbius strip and provide visual proofs of these properties using exploration techniques. The experiments include constructing the objects, observing their properties, and explaining via experiments that altering the objects by cutting them does not preserve their hereditary properties.