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Step 4: Rectangle Translation Tessellation

Step 4: Rectangle Translation Tessellation
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2014-03-30 03:40
PolygonVectorCoordinate GeometryGeometric Construction
In collections Tess 1
This example demonstrates the fourth step in constructing a rectangle translation tessellation, focusing on vector translation to create new rectangles and complete the pattern. Key math concepts include vectors, translation transformations, polygon construction, and coordinate geometry. GeoGebra commands like Segment, OrthogonalLine, Point, Intersect, Polygon, and Vector, especially Translate, are used to construct the tessellation. Suitable for high school mathematics education to illustrate geometric transformations and tessellation patterns.

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(A, C) → e
  8. Segment(C, D) → f
  9. Segment(D, B) → g
  10. Polygon(A, B, D, C) → poly1, a_1, b_1, d_1, c_1
  11. Segment(A_1, B_1) → a_2
  12. Segment(E_1, F_1) → i_1
  13. Segment(F_1, G_1) → j_1
  14. Segment(G_1, H_1) → k_1
  15. Segment(H_1, I_1) → l_1
  16. Segment(A, F_1) → h
  17. Segment(F_1, G_1) → i
  18. Segment(G_1, H_1) → j
  19. Segment(H_1, I_1) → k
  20. Segment(I_1, B) → l
  21. Vector(A, C) → u
  22. Translate(A, u) → A'
  23. Translate(F_1, u) → E
  24. Segment(A', E) → h'
  25. Translate(F_1, u) → F
  26. Translate(G_1, u) → G
  27. Segment(F, G) → i'
  28. Translate(G_1, u) → H
  29. Translate(H_1, u) → I
  30. Segment(H, I) → j'
  31. Translate(H_1, u) → J
  32. Translate(I_1, u) → K
  33. Segment(J, K) → k'
  34. Translate(I_1, u) → L
  35. Translate(B, u) → B'
  36. Segment(L, B') → l'
  37. Segment(A, M) → m
  38. Segment(M, A) → n
  39. Segment(M, N) → p
  40. Segment(N, O) → q
  41. Segment(O, P) → r
  42. Segment(P, Q) → s
  43. Segment(Q, R) → t
  44. Segment(R, S) → e_1
  45. Segment(S, T) → f_1
  46. Segment(T, U) → g_1
  47. Segment(U, V) → h_1
  48. Segment(V, C) → m_1
  49. Vector(C, D) → v
  50. Translate(A', v) → A''
  51. Translate(A, v) → A'_1
  52. Translate(M, v) → M'
  53. Segment(A'_1, M') → m'
  54. Translate(M, v) → M'_1
  55. Translate(A, v) → A'_2
  56. Segment(M'_1, A'_2) → n'
  57. Translate(M, v) → M'_2
  58. Translate(N, v) → N'
  59. Segment(M'_2, N') → p'
  60. Translate(N, v) → N'_1
  61. Translate(O, v) → O'
  62. Segment(N'_1, O') → q'
  63. Translate(O, v) → O'_1
  64. Translate(P, v) → P'
  65. Segment(O'_1, P') → r'
  66. Translate(P, v) → P'_1
  67. Translate(Q, v) → Q'
  68. Segment(P'_1, Q') → s'
  69. Translate(Q, v) → Q'_1
  70. Translate(R, v) → R'
  71. Segment(Q'_1, R') → t'
  72. Translate(R, v) → R'_1
  73. Translate(S, v) → S'
  74. Segment(R'_1, S') → n_1
  75. Translate(S, v) → S'_1
  76. Translate(T, v) → T'
  77. Segment(S'_1, T') → p_1
  78. Translate(T, v) → T'_1
  79. Translate(U, v) → U'
  80. Segment(T'_1, U') → q_1
  81. Translate(U, v) → U'_1
  82. Translate(V, v) → V'
  83. Segment(U'_1, V') → r_1
  84. Translate(V, v) → V'_1
  85. Translate(C, v) → C'
  86. Segment(V'_1, C') → s_1

AI Drawing Prompt Reference

Draw a rectangle and create new rectangles by vector translation to complete a tessellation pattern. Start with a line segment, then draw perpendicular lines from both ends to find intersection points. Connect these points to form new rectangles, and repeat the translation process to expand the pattern, demonstrating vectors and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.