Dynamic Differential Geometry in Education

By Hannes Kaufmann

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.

Reference

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

BibTeX

@article{TUW-176091,     author = {Kaufmann, Hannes},     title = {Dynamic Differential Geometry in Education},     journal = {Journal for Geometry and Graphics},     year = {2009},     volume = {13},     number = {2},     url = {http://publik.tuwien.ac.at/files/PubDat_176091.pdf},     keywords = {Di erential geometry, dynamic three-dimensional geometry, augmented reality, geometry education} } Click into the text area and press Ctrl+A/Ctrl+C or ⌘+A/⌘+C to copy the BibTeX into your clipboard… or download the BibTeX.