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# 111020 analytic geometry

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### 111020 analytic geometry

1. 1. Understanding versus Procedure Analytic Geometry Martin Zacharias
2. 2. Understanding? Comprehension?
3. 3. Everyday life in school <ul><li>Given are to lines and </li></ul><ul><ul><li>a) Which situation do they have? Find the points of intersection. </li></ul></ul><ul><ul><li>b) Describe the plane E, which includes the lines g and h. </li></ul></ul><ul><ul><li>c) Find a line, which has no points of intersection with g and h. Give the reason for your choice. </li></ul></ul><ul><ul><li>d) Find the points of intersection to the basic-planes (xy-plane, xz-plane and yz-plane) and draw the lines g and h. </li></ul></ul><ul><ul><li>Draw the point of intersection of both lines. </li></ul></ul><ul><ul><li>e) Find the angle between g and h. </li></ul></ul><ul><ul><li>f) Find the angle between the basic-planes. </li></ul></ul><ul><ul><li>… </li></ul></ul>
4. 4. Everyday life in school?
5. 5. <ul><li>The exercise isn’t to bad. You have to argue, you have do draw. </li></ul><ul><li>But the finding of terms and equations and the calculation with equations is dominant. </li></ul><ul><li>Geometry and basis ideas don’t exist. </li></ul>
6. 6.
7. 7. Vertical lines
8. 8. Distance
9. 9. Circle (0|0) with radius 4
10. 10. Descartes Dictionary
11. 11. <ul><li>We need activities for the pupils. </li></ul>
12. 12. Concept by Objects <ul><li>From doing to thinking in three steps </li></ul><ul><li>to comprehend the real model (situation) </li></ul><ul><li>to represent und describe it in a drawing </li></ul><ul><li>to represent and describe it in the analytic model </li></ul>
13. 13. Crossing section on a cube
14. 14. Diagonals
15. 15.
16. 16. 2D of real objects
17. 17. Forms of a roof
18. 18. Read out the point
19. 19. S is the summit of a pyramid
20. 20. half of a cube
21. 21.
22. 22.
23. 23. Cross-sections by liquids
24. 24. Cross-section of a regular Hexagon
25. 25. Werkzeug -CD F:VortragKiel_100922CD_AnaGeostart.htm
26. 26. Schrägbilddarstellungen
27. 27. Corner of a cube C=(8|3|6), F=(2|9|6), G=(4|5|10), H=(0|1|8)
28. 28. Vector
29. 29. Vectors in objects
30. 30. Vectors in objects
31. 31. Regular Hexagon in a cube
32. 32. Regular Hexagon in an Oktaeder
33. 33. Rectangle in a cube Center of the cube – center of the rectangle.
34. 34. Cross-section
35. 35. Diagonals in the space
36. 36. Mittendreieck
37. 37.
38. 38.
39. 39. Lines in the space
40. 40. Lagebeziehung von Geraden im Raum
41. 41.
42. 42. Area in a roof (Walmdach) Describe the blue area with lines.
43. 43. Line segments in a Pyramid
44. 44. „ Haus des Nikolaus“
45. 45. Cube with a cut off corner
46. 46. Cut off cube (Kuboktaeder)
47. 47. Position of lines
48. 48. Point of intersection? No, it doesn’t exist a point of intersection.
49. 49. Lagebeziehung mit GTR
50. 50. Lagebeziehung und GTR
51. 51. Ebenen im Raum
52. 52. experiment - search
53. 53.
54. 54. Ebene - experimentell
55. 55. Objektstudie
56. 56.
57. 57. What happens, when … ? <ul><li>… B goes towards F with the angle beta? </li></ul>