1. CADGME conference, Linz. JULY 2009 1/12 TEACHING COMPUTER AIDED DESIGN WITH THE USE OF DYNAMIC GEOMETRY Francisco Pérez Universidad Politécnica de Madrid. Spain

2. CADGME conference, Linz. JULY 2009 2/12 Introduction Geometry at university level The discipline of CAD Why Geogebra? Examples Conclusions Contents Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions

3. CADGME conference, Linz. JULY 2009 3/12 CAD with commercial programs + Business, - Teaching Little knowledge on how CAD works Consolidate theoretical concepts and acquire practice Introduction (I) Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions

4. CADGME conference, Linz. JULY 2009 4/12 Introduction (II) Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions Bezier, B-Splines, NURBS curves: properties DGS. Algorithms DGS Surfaces CAD programs Why? Develop specific applications

5. CADGME conference, Linz. JULY 2009 5/12 Geometry contents very different Geometry contents reduced CAD: not only buttons, but algorithms Shipyard: CAD user, CAD application developer DGS: multimedia contents DGS shows to be an attractive and effective way to develop spatial abilities Geometry at university level Technical Drawing Basic CAD Descriptive Geometry CAD (Comp. Geometry) Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions

6. CADGME conference, Linz. JULY 2009 6/12 1962 Sketchpad 60’s Bézier, Casteljau 1985 NURBS software CAD is taught very differently: programs, geometric,… CAD can not exist without commercial CAD programs Capacity to use CAD tools, and develop programs CAD algorithms will be the same, not the programs The discipline of CAD Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions

7. CADGME conference, Linz. JULY 2009 7/12 Algorithms graphically and analytically Free Step by step Why Geogebra? (I) Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions

8. CADGME conference, Linz. JULY 2009 8/12 Geometric commands important for CAD Why Geogebra? (II) Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions

9. CADGME conference, Linz. JULY 2009 9/12 NURBS (Non Uniform Rational B-splines): algebraically NURBS (Nobody Understand Rational B-splines) Examples (I) Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions

10. CADGME conference, Linz. JULY 2009 10/12 Conics as NURBS Examples (II) Projective geometry Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions

11. CADGME conference, Linz. JULY 2009 11/12 DGS: understanding algorithms bellow CAD programs DGS: active learning, not push buttons, not black boxes Classes as laboratories More time on class preparation, more time for students CAD programs are necessary CAD+DGS = positive for developers and programmers Conclusions Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions

12. CADGME conference, Linz. JULY 2009 12/12 Thank you! Thank you! Introduction Geometry at University level The discipline of CAD Why Geogebra? Examples Conclusions