This workshop was designed for students enrolled in the Master in Mathematics Teacher Education for Middle and Secondary Schools—a program focused on the academic and professional training of mathematics teachers from the Mathematics Department of the Faculty of Sciences of the University of Porto. The initiative aimed to create an experimental environment to explore concepts and results of Spherical Geometry through drawing-based activities.

The central theme focusedon the concept of a right triangle on the sphere, which is crucial for stating the geometrical Spherical Pythagorean Theorem. The typical generalization of a right triangle on the sphere—a triangle with at least one right angle—leads to discrepancies between right triangles in the plane and in spherical geometry. The main goal was to explorealternative definitions of aright triangle in the spherethat align more closely withtheir counterparts in the Euclidean plane. This was achieved by exploring some fundamental principles of spherical geometry employing three distinct scales, drawing tools, and supports: a Lénárt sphere, paper, and a blackboard. Prior to all else, the workshop began with learning to draw a sphere. To achieve this, the concept of projection was introduced, employing the model derived from the study of conic sections.

Furthermore, this experience aimed to demonstrate to future teachers the feasibility of these tools in a classroom context.