Ball Geometry as a New Trend in Geometry Education

About

Ball Geometry is based on Comparative Geometry on the plane and on the sphere. We study two different geometric systems, not sequentially but simultaneously, constantly comparing one with the other. Instead of a Euclidean monologue, we engage in an exciting drama between two different worlds of geometry.

We begin with elementary concepts of Euclidean plane geometry, such as points, lines, circles, distance, angle, etc., contrasting them with their counterparts on the surface of a sphere. We then explore more advanced concepts of synthetic spherical geometry, and conclude the course with a brief overview of Bolyai-Gauss-Lobachevskian hyperbolic geometry

Target group

No prerequisite knowledge of Non-Euclidean geometries is required to complete the course

Course aim

Comparative Geometry of the Plane and the Sphere is an educational project already known to many experts in mathematics education worldwide. The target audience ranges from elementary schools to tertiary education and in-service teacher training. It is aimed not only at math enthusiasts, but also at those indifferent or even hostile to the subject.

Activities in the classroom are mostly based on manual experiments with planar and spherical ruler, compass and protractor, or round-shaped fruits, with minimal use of virtual aids.

Discussion or debate between peers plays a crucial role in the learning process. The emphasis is on the independent creation of mathematical concepts rather than passive reception.

Spherical geometry is closely related to other subjects, such as geography and astronomy, but physics, chemistry and visual arts also benefit from it.

The project began in Hungary in the eighties, and has been continuously present among elective courses at Eötvös Loránd University since 1990 for future teachers from kindergarten to high school, and even university studies.

Comparing different systems of geometry helps the learner to apply this approach to other paths of life, to step out from one fixed perspective to tolerance toward and understanding of those who are different in their cultural, traditional, or social background. Our greatest hope is that studying comparative geometry may increase the number of people with whom the learner can communicate, live and work on this tiny Earth-globe

Fee info