Combing: The Hair of a Hairy Ball?. Geometry with the Hairy Ball Theorem: A Practical Proposal for Bringing the Sphere into the Mathematics Classroom
This research article addresses the application of the Hairy Ball Theorem in the teaching of geometry, proposing a practical activity to bring the concept of the sphere closer to the students. The Hairy Ball Theorem states that it is always possible to comb the hair of a hairy ball without leaving any unruly strands. This interesting topological property has implications in geometry and can be used as a teaching resource to promote understanding of the characteristics and properties of the sphere. In addition to encouraging hands-on manipulation and experimentation, this activity seeks to develop spatial reasoning skills, visualization, and understanding of geometric concepts. Students can observe how properties of the sphere, such as symmetry and constant curvature, influence the way the hair on the furry ball can be combed. It is hoped that this hands-on approach can help educators approach the geometry of the sphere in a more tangible and engaging way for students. In addition, this activity can encourage students’ interest and active participation in mathematics classes.
