Dynamic Differential Geometry in Education

We present an augmented reality application which introduces differentialgeometry in educational dynamic geometry software. New functionalitysuch as a Frenet frame, center and circle of curvature in arbitrary curve points,and others were implemented. Dynamic geometry allows to study di erential geometricproperties under movement. Using this tool we developed examples whichenable teachers and learners to intuitively explore properties of interesting curves,to visualize contact of higher order between curves and surfaces, to constructMeusnier's sphere, Dupin's indicatrix and more.