1 / 29

Jean-Jacques Dahan jjdahan@wanadoo.fr IREM of Toulouse

14 de T 3 Europe Symposium . Oostende 22-23/08/2011. A Dynamic Approach of Analytic Geometry in 3D with TI N’Spire Enhancing an Experimental Process of Discovery. Jean-Jacques Dahan jjdahan@wanadoo.fr IREM of Toulouse. INTRODUCTION.

cheng
Download Presentation

Jean-Jacques Dahan jjdahan@wanadoo.fr IREM of Toulouse

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 14de T3 Europe Symposium Oostende 22-23/08/2011 A Dynamic Approach of Analytic Geometry in 3D with TI N’SpireEnhancing an Experimental Process of Discovery Jean-JacquesDahan jjdahan@wanadoo.fr IREM of Toulouse

  2. INTRODUCTION Representing 3D objects in 2D withtwoparallel perspectives

  3. The « cavaliere » and the « military » perspectives « Cavaliere » perspective « Military » perspective PC.cg3 PM.cg3

  4. Theses perspectives with dynamic numbers in the « Geometry » application of TI N’Spire Paper1 problem 1

  5. An example of representation Circles in base planes Paper1 problem 1

  6. Another example using dynamic numbers: Dynamic coordinates for movable points Paper 1 problem 2

  7. PART 1 CYLINDERS and CONES Theirrepresentations in « cavaliere » and « military » perspectives

  8. With traces and loci Paper1 problems 3, 4

  9. PART 2FOLDING and UNFOLDING In « military » perspective

  10. Folding and unfoldingcylindersin « military » perspective

  11. The technique Paper1 problems 5

  12. The result Paper1 problems 5

  13. Folding and unfoldingconesin « military » perspective

  14. The model Paper2 problem 1

  15. PART 3The experimentalprocess of discoverywithtechnology Two conjectures obtainedwith the model of unfolding a cone and theirproofs

  16. Unfolding a cone onto half a disk Paper2 problems2

  17. Formal proof

  18. Evaluation of a limit of a ratio (betweentwo angles) Paper2 problem 3

  19. Formal proof

  20. PART 4SURFACES z = f(x,y) Two possible approaches

  21. With the « Graphs » application of TI N’Spire

  22. Paper3 problem1

  23. Paper3 problem 2

  24. With the « 3D Graphing » toolof TI N’Spire

  25. z = sin(x)+cos(y) z = 0 Paper3 problem 3

  26. z = sin(x)+cos(y) z = 0 Paper3 problem 4

  27. CONCLUSIONas a new title Dynamicnumbers for a dynamicapproach of 3D analyticgeometry

  28. z = sin(x)- k.cos(y) Paper3 problem5

  29. Dank u wel! jjdahan@wanadoo.fr

More Related