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Translation Tessellation Step 9

Translation Tessellation Step 9
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2014-03-28 10:12
PolygonVectorTransformationGeometric Construction
In collections Translation Tesselation
This example demonstrates the construction of a geometric pattern using translation operations, specifically showing how vector transformations and geometric transformations can generate complex fractal structures. Core mathematical concepts include vectors, translation transformations, polygon construction, and analytical geometry. Key GeoGebra commands and objects used in the construction, as derived from the construction summary, are Polygon, Segment, Vector, Translate, Intersect, Point, and Circle. Suitable for high school and above learners to understand the application of geometric transformations in art and design, as well as exploring the principles of fractal geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Segment(A, E) → e
  3. Segment(E, F) → f
  4. Segment(F, G) → g
  5. Segment(G, H) → h
  6. Segment(J, B) → k
  7. Segment(H, J) → i
  8. Vector(A, D) → u
  9. Translate(A, u) → A'
  10. Translate(E, u) → E'
  11. Segment(A', E') → e'
  12. Translate(E, u) → E'_1
  13. Translate(F, u) → F'
  14. Segment(E'_1, F') → f'
  15. Translate(F, u) → F'_1
  16. Translate(G, u) → G'
  17. Segment(F'_1, G') → g'
  18. Translate(G, u) → G'_1
  19. Translate(H, u) → H'
  20. Segment(G'_1, H') → h'
  21. Translate(J, u) → J'
  22. Translate(B, u) → B'
  23. Segment(J', B') → k'
  24. Translate(H, u) → H'_1
  25. Translate(J, u) → J'_1
  26. Segment(H'_1, J'_1) → i'
  27. Segment(D, I) → j
  28. Segment(I, K) → l
  29. Segment(K, L) → m
  30. Segment(L, M) → n
  31. Segment(M, N) → p
  32. Segment(N, A) → q
  33. Vector(A, B) → v
  34. Translate(A, v) → A'_1
  35. Translate(E, v) → E'_2
  36. Segment(A'_1, E'_2) → e'_1
  37. Translate(A', v) → A''
  38. Translate(E', v) → E''
  39. Segment(A'', E'') → e''
  40. Translate(D, v) → D'
  41. Translate(I, v) → I'
  42. Segment(D', I') → j'
  43. Translate(I, v) → I'_1
  44. Translate(K, v) → K'
  45. Segment(I'_1, K') → l'
  46. Translate(K, v) → K'_1
  47. Translate(L, v) → L'
  48. Segment(K'_1, L') → m'
  49. Translate(L, v) → L'_1
  50. Translate(M, v) → M'
  51. Segment(L'_1, M') → n'
  52. Translate(M, v) → M'_1
  53. Translate(N, v) → N'
  54. Segment(M'_1, N') → p'
  55. Translate(N, v) → N'_1
  56. Translate(A, v) → A'_2
  57. Segment(N'_1, A'_2) → q'
  58. Intersect(f, g) → O
  59. Intersect(g, h) → P
  60. Point(i) → Q
  61. Intersect(k, i) → R
  62. Intersect(p', q') → S
  63. Intersect(n', p') → T
  64. Intersect(m', n') → U
  65. Intersect(l', m') → V
  66. Intersect(j', l') → W
  67. Intersect(k', i') → Z
  68. Intersect(h', i') → A_1
  69. Intersect(g', h') → B_1
  70. Intersect(f', g') → C_1
  71. Point(l) → D_1
  72. Intersect(l, m) → E_1
  73. Intersect(m, n) → F_1
  74. Intersect(n, p) → G_1
  75. Intersect(p, q) → H_1
  76. Polygon(A, O, W, C, Z, A_1, B_1, C_1, D, D_1, E_1, F_1, P, G_1, H_1, Q, R, B, S, T, U, V) → poly2, a_1, v_1, w, c_1, z, a_2, b_2, c_2, d_1, d_2, e_1, o, f_1, g_1, h_1, p_1, q_1, r, b_1, s, t, u_1
  77. Circle(I_1, J_1) → k_1
  78. Intersect(n', p') → K_1
  79. Intersect(m', n') → L_1
  80. Point(m') → M_1
  81. Point(n') → N_1
  82. Point(n') → P_1
  83. Point(n') → R_1
  84. Polygon(K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1) → poly3, k_2, l_1, m_1, n_1, o_1, p_2, q_2, r_1, s_1
  85. Intersect(n, p) → T_1
  86. Intersect(m, n) → U_1
  87. Polygon(T_1, U_1, V_1, W_1, Z_1, A_2, B_2) → poly4, t_1, u_2, v_2, w_1, z_1, a_3, b_3

AI Drawing Prompt Reference

Draw a geometric pattern consisting of a quadrilateral and multiple line segments, start by drawing a quadrilateral, then draw four line segments from one vertex of the quadrilateral, use vector translation to move the quadrilateral and line segments in the direction of the vector, generating a series of new quadrilaterals and line segments, finally combine these shapes to form a complex geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.