Journal for Geometry and Graphics 13 (2009), No. 2, 241--254
Copyright Heldermann Verlag 2009
Dynamic Differential Geometry in Education
Hannes Kaufmann
Institute of Software Technology and Interactive Systems, Technical University, Favoritenstr. 9-11/118/2, 1040 Wien, Austria
kaufmann@ims.tuwien.ac.at
We present an augmented reality application which introduces differential geometry in educational dynamic geometry software. New functionality such as a Frenet frame, center and circle of curvature in arbitrary curve points, and others were implemented. Dynamic geometry allows to study differential geometric properties under movement. Using this tool we developed examples which enable teachers and learners to intuitively explore properties of interesting curves, to visualize contact of higher order between curves and surfaces, to construct Meusnier's sphere, Dupin's indicatrix and more.
Keywords: Differential geometry, dynamic three-dimensional geometry, augmented reality, geometry education.
MSC: 53A04; 53A05, 68U05
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