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Tessellation from Rectangle

Tessellation from Rectangle
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2013-07-12 06:19
VectorTransformationGeometric Construction
In collections Tessellation from Rectangle using Translation
This example demonstrates how to generate a tessellation pattern starting from a rectangle using geometric transformations. Key mathematical concepts include geometric construction, vectors, and translation. Using commands like Segment, OrthogonalLine, Point, Intersect, Vector, and Translate, complex geometric shapes can be constructed. Suitable for middle school and above students to learn about geometric transformations and tessellations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Segment(C, A) → e
  8. Segment(D, B) → f
  9. Segment(C, D) → g
  10. Segment(A, E) → h
  11. Segment(E, F) → i
  12. Segment(F, G) → j
  13. Segment(G, H) → k
  14. Segment(H, C) → l
  15. Vector(C, D) → u
  16. Translate(C, u) → C'
  17. Translate(A, u) → A'
  18. Segment(C', A') → e'
  19. Translate(A, u) → A'_1
  20. Translate(E, u) → E'
  21. Segment(A'_1, E') → h'
  22. Translate(E, u) → E'_1
  23. Translate(F, u) → F'
  24. Segment(E'_1, F') → i'
  25. Translate(F, u) → F'_1
  26. Translate(G, u) → G'
  27. Segment(F'_1, G') → j'
  28. Translate(G, u) → G'_1
  29. Translate(H, u) → H'
  30. Segment(G'_1, H') → k'
  31. Translate(H, u) → H'_1
  32. Translate(C, u) → C'_1
  33. Segment(H'_1, C'_1) → l'
  34. Segment(A, I) → m
  35. Segment(I, J) → n
  36. Segment(J, K) → p
  37. Segment(K, L) → q
  38. Segment(L, M) → r
  39. Segment(M, B) → s
  40. Vector(A, C) → v
  41. Translate(A, v) → A'_2
  42. Translate(B, v) → B'
  43. Segment(A'_2, B') → a'
  44. Translate(A, v) → A'_3
  45. Translate(I, v) → I'
  46. Segment(A'_3, I') → m'
  47. Translate(I, v) → I'_1
  48. Translate(J, v) → J'
  49. Segment(I'_1, J') → n'
  50. Translate(J, v) → J'_1
  51. Translate(K, v) → K'
  52. Segment(J'_1, K') → p'
  53. Translate(K, v) → K'_1
  54. Translate(L, v) → L'
  55. Segment(K'_1, L') → q'
  56. Translate(L, v) → L'_1
  57. Translate(M, v) → M'
  58. Segment(L'_1, M') → r'
  59. Translate(M, v) → M'_1
  60. Translate(B, v) → B'_1
  61. Segment(M'_1, B'_1) → s'
  62. Translate(A', v) → A''
  63. Translate(A'_1, v) → O