Dynamic Differential Geometry in Education

H. Kaufmann:
"Dynamic Differential Geometry in Education";
Journal for Geometry and Graphics,13(2009), 2.

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Abstract:


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 di erential 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.