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Connectivity Matrix

Connectivity Matrix
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2017-11-20 16:35
PolygonMatrixTransformation
In collections Solids, graphs and paths
This example demonstrates the concept of a connectivity matrix, involving core mathematical concepts of matrices and transformations. Using GeoGebra commands such as Polygon, Mirror, Point, and Line, it constructs a polygon and its mirror image, illustrating how a connectivity matrix describes the relationships between shapes. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → vierhoek1, a, b, c, d
  2. Mirror(A, B) → A'
  3. Mirror(B, B) → B'
  4. Mirror(C, B) → C'
  5. Mirror(D, B) → D'
  6. Polygon(A', B', C', D') → vierhoek1', a', b', c', d'
  7. Point(yAxis) → E_1
  8. Point(xAxis) → F_1
  9. Line(E_1, F_1) → f
  10. Mirror(A, A) → A'_1
  11. Mirror(B, A) → B'_1
  12. Mirror(C, A) → C'_1
  13. Mirror(D, A) → D'_1
  14. Polygon(A'_1, B'_1, C'_1, D'_1) → vierhoek1'_1, a'_1, b'_1, c'_1, d'_1
  15. Point(xAxis) → G_1
  16. Line(G_1, E_1) → g
  17. Mirror(A, C) → A'_2
  18. Mirror(B, C) → B'_2
  19. Mirror(C, C) → C'_2
  20. Mirror(D, C) → D'_2
  21. Polygon(A'_2, B'_2, C'_2, D'_2) → vierhoek1'_2, a'_2, b'_2, c'_2, d'_2
  22. Mirror(A, D) → A'_3
  23. Mirror(B, D) → B'_3
  24. Mirror(C, D) → C'_3
  25. Mirror(D, D) → D'_3
  26. Polygon(A'_3, B'_3, C'_3, D'_3) → vierhoek13, a'_3, b'_3, c'_3, d'_3
  27. Point(yAxis) → H_1
  28. Line(G_1, H_1) → i
  29. Line(H_1, F_1) → j
  30. Rotate(vierhoek1', (-(90°)), f) → vierhoek12
  31. Rotate(vierhoek1'_2, 90°, j) → vierhoek2
  32. Rotate(vierhoek13, 90°, i) → vierhoek3
  33. Rotate(vierhoek1'_1, (-(90°)), g) → vierhoek4
  34. Rotate(D', (-(90°)), f) → J
  35. Translate(vierhoek1, Vector[(0, 0, z(J))]) → vierhoek14
  36. Rotate(C', (-(90°)), f) → E
  37. Rotate(C'_1, (-(90°)), g) → I
  38. Rotate(C'_3, 90°, i) → H
  39. Rotate(B'_3, 90°, i) → L
  40. Rotate(B'_2, 90°, j) → G
  41. Rotate(A'_2, 90°, j) → K
  42. Rotate(A', (-(90°)), f) → F
  43. Polygon(J, F, K) → driehoek1, m, d'', a''
  44. Polygon(B, C, F) → driehoek2, a''_1, b_1, c_1
  45. Polygon(K, G, L) → driehoek3, k, m_1, l
  46. Polygon(C, D, G) → driehoek4, l_1, c_2, d_1
  47. Polygon(L, H, I) → driehoek5, i_1, k_1, j_1
  48. Polygon(A, H, D) → driehoek6, d_2, a_1, j_2
  49. Point(ribben3) → P
  50. TableText({{"A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L"}}) → tekst1
  51. TableText({{"A"}, {"B"}, {"C"}, {"D"}, {"E"}, {"F"}, {"G"}, {"H"}, {"I"}, {"J"}, {"K"}, {"L"}}) → tekst2