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Tessellation by Translation

Tessellation by Translation
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2014-06-28 01:25
PolygonVectorTransformation
In collections Transformations
This example demonstrates how to create a tessellation of regular polygons on a plane using translation. Key mathematical concepts include translation, coordinates, and regular polygons. Using GeoGebra commands such as Polygon, Vector, and Translate, multiple regular polygons are constructed and translated to form a beautiful tessellation pattern. Suitable for middle school and above students to learn about geometric transformations and tessellations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 8) → poly1, a, D, E, F, G, H, b, c, d, e, f, g, h, C
  2. Polygon(B, A, 4) → poly2, i, j, k, l, I, J
  3. Polygon(I, A, H, G, F, E, D, C, B, J) → poly3, i_1, j_1, a_1, h_1, g_1, f_1, e_1, d_1, c_1, b_1
  4. Vector(F, C) → u
  5. Translate(I, u) → I'
  6. Translate(A, u) → A'
  7. Translate(H, u) → H'
  8. Translate(G, u) → G'
  9. Translate(F, u) → F'
  10. Translate(E, u) → E'
  11. Translate(D, u) → D'
  12. Translate(C, u) → C'
  13. Translate(B, u) → B'
  14. Translate(J, u) → J'
  15. Polygon(I', A', H', G', F', E', D', C', B', J') → poly3', i', j', a', h', g', f', e', d', c', b'
  16. Vector(H, E') → v
  17. Translate(I, v) → I'_1
  18. Translate(A, v) → A'_1
  19. Translate(H, v) → H'_1
  20. Translate(G, v) → G'_1
  21. Translate(F, v) → F'_1
  22. Translate(E, v) → E'_1
  23. Translate(D, v) → D'_1
  24. Translate(C, v) → C'_1
  25. Translate(B, v) → B'_1
  26. Translate(J, v) → J'_1
  27. Polygon(I'_1, A'_1, H'_1, G'_1, F'_1, E'_1, D'_1, C'_1, B'_1, J'_1) → poly3'_1, i'_1, j'_1, a'_1, h'_1, g'_1, f'_1, e'_1, d'_1, c'_1, b'_1
  28. Vector(J', E') → w
  29. Translate(I', w) → I''
  30. Translate(A', w) → A''
  31. Translate(H', w) → H''
  32. Translate(G', w) → G''
  33. Translate(F', w) → F''
  34. Translate(E', w) → E''
  35. Translate(D', w) → D''
  36. Translate(C', w) → C''
  37. Translate(B', w) → B''
  38. Translate(J', w) → J''
  39. Polygon(I'', A'', H'', G'', F'', E'', D'', C'', B'', J'') → poly3'', i'', j'', a'', h'', g'', f'', e'', d'', c'', b''
  40. Vector(F'_1, C') → m
  41. Translate(I'_1, m) → K
  42. Translate(A'_1, m) → L
  43. Translate(H'_1, m) → M
  44. Translate(G'_1, m) → N
  45. Translate(F'_1, m) → O
  46. Translate(E'_1, m) → P
  47. Translate(D'_1, m) → Q
  48. Translate(C'_1, m) → R
  49. Translate(B'_1, m) → S
  50. Translate(J'_1, m) → T
  51. Polygon(K, L, M, N, O, P, Q, R, S, T) → poly4, k_1, t, l_1, m_1, n, o, p, q, r, s
  52. Vector(F, I) → u_1
  53. Translate(I, u_1) → I'_2
  54. Translate(A, u_1) → A'_2
  55. Translate(H, u_1) → H'_2
  56. Translate(G, u_1) → G'_2
  57. Translate(F, u_1) → F'_2
  58. Translate(E, u_1) → E'_2
  59. Translate(D, u_1) → D'_2
  60. Translate(C, u_1) → C'_2
  61. Translate(B, u_1) → B'_2
  62. Translate(J, u_1) → J'_2
  63. Polygon(I'_2, A'_2, H'_2, G'_2, F'_2, E'_2, D'_2, C'_2, B'_2, J'_2) → poly3'_2, i'_2, j'_2, a'_2, h'_2, g'_2, f'_2, e'_2, d'_2, c'_2, b'_2
  64. Vector(B, B'_1) → v_1
  65. Translate(I', v_1) → I''_1
  66. Translate(A', v_1) → A''_1
  67. Translate(H', v_1) → H''_1
  68. Translate(G', v_1) → G''_1
  69. Translate(F', v_1) → F''_1
  70. Translate(E', v_1) → E''_1
  71. Translate(D', v_1) → D''_1
  72. Translate(C', v_1) → C''_1
  73. Translate(B', v_1) → B''_1
  74. Translate(J', v_1) → J''_1
  75. Polygon(I''_1, A''_1, H''_1, G''_1, F''_1, E''_1, D''_1, C''_1, B''_1, J''_1) → poly3''_1, i''_1, j''_1, a''_1, h''_1, g''_1, f''_1, e''_1, d''_1, c''_1, b''_1
  76. Vector(C, I') → w_1
  77. Translate(I', w_1) → I''_2
  78. Translate(A', w_1) → A''_2
  79. Translate(H', w_1) → H''_2
  80. Translate(G', w_1) → G''_2
  81. Translate(F', w_1) → F''_2
  82. Translate(E', w_1) → E''_2
  83. Translate(D', w_1) → D''_2
  84. Translate(C', w_1) → C''_2
  85. Translate(B', w_1) → B''_2
  86. Translate(J', w_1) → J''_2
  87. Polygon(I''_2, A''_2, H''_2, G''_2, F''_2, E''_2, D''_2, C''_2, B''_2, J''_2) → poly3''_2, i''_2, j''_2, a''_2, h''_2, g''_2, f''_2, e''_2, d''_2, c''_2, b''_2

AI Drawing Prompt Reference

Create a hexagonal tessellation pattern using regular octagons and squares. Start by drawing a regular octagon with points A and B, then draw a square with points B and A. Use vector u from point F to C to translate the square and octagon, forming new shapes. Repeat this process using vector v from point H to E' to translate the previous shapes. Finally, use vector m from point F'_1 to C' to translate the latest shapes, completing the tessellation pattern.
The prompt above was compiled from the original drawing commands and is for reference only.