Tessellation by Translation by jahatch8

Tessellation by Translation by jahatch8
Loading the math board and drawing, please wait…
2014-03-30 05:24
This example demonstrates the process of generating a tessellation through translation. Key mathematical concepts include translation transformation and geometric construction. It uses commands like Polygon, AttachCopyToView, Point, Vector, Translate, etc. Suitable for middle school and above students to learn about geometric transformations and tessellations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. AttachCopyToView(PolyLine[(2.86, -2.88), (2.7800000000000002, -2.88), (2.7, -2.88), (2.62, -2.9), (2.56, -2.94), (2.52, -3), (2.48, -3.06), (2.44, -3.12), (2.4, -3.18), (2.38, -3.24), (2.36, -3.3000000000000003), (2.36, -3.38), (2.36, -3.46), (2.36, -3.54), (2.36, -3.62), (2.3000000000000003, -3.68), (2.24, -3.7), (2.18, -3.72), (2.12, -3.74), (2.06, -3.7600000000000002), (1.98, -3.8200000000000003), (1.92, -3.86), (1.86, -3.92), (1.8, -3.96), (1.74, -4.0200000000000005), (1.6600000000000001, -4.0200000000000005), (1.6, -4.08), (1.54, -4.1), (1.5, -4.16), (1.44, -4.22), (1.42, -4.28), (1.4000000000000001, -4.34), (1.4000000000000001, -4.42), (1.3800000000000001, -4.48), (1.32, -4.44), (1.32, -4.34), (1.3, -4.28), (1.3, -4.2), (1.3, -4.12), (1.3, -4.04), (1.32, -3.98), (1.34, -3.92), (1.4000000000000001, -3.86), (1.46, -3.8200000000000003), (1.54, -3.8200000000000003), (1.56, -3.7600000000000002), (1.6, -3.7), (1.6600000000000001, -3.66), (1.72, -3.6), (1.78, -3.58), (1.84, -3.54), (1.9000000000000001, -3.5), (1.84, -3.48), (1.76, -3.48), (1.7, -3.46), (1.6400000000000001, -3.44), (1.58, -3.4), (1.52, -3.36), (1.46, -3.3000000000000003), (1.44, -3.24), (1.44, -3.16), (1.44, -3.08), (1.44, -3), (1.44, -2.92), (1.44, -2.84), (1.46, -2.7600000000000002), (1.48, -2.7), (1.52, -2.64), (1.56, -2.58), (1.58, -2.52), (1.6400000000000001, -2.48), (1.58, -2.5), (1.52, -2.52), (1.44, -2.52), (1.36, -2.52), (1.28, -2.52), (1.2, -2.52), (1.1400000000000001, -2.5), (1.08, -2.48), (1.04, -2.42), (1, -2.36), (0.96, -2.3000000000000003), (0.9, -2.24), (0.9, -2.16), (0.86, -2.1), (0.86, -2.02), (0.84, -1.96), (0.84, -1.8800000000000001), (0.78, -1.86), (0.76, -1.92), (0.7000000000000001, -1.94), (0.64, -1.96), (0.58, -1.98), (0.52, -2), (0.44, -2.02), (0.34, -2.02), (0.26, -2.02), (0.2, -2), (0.16, -1.94), (0.12, -1.8800000000000001), (0.1, -1.82), (0.06, -1.76), (0, -1.72), (-0.06, -1.76), (-0.1, -1.82), (-0.16, -1.84), (-0.18, -1.9000000000000001), (-0.24, -1.94), (-0.3, -1.98), (-0.36, -2.02), (-0.42, -2.04), (-0.5, -2.04), (-0.58, -2.04), (-0.6, -1.98), (-0.62, -1.92), (-0.64, -1.86), (-0.64, -1.78), (-0.64, -1.7), (-0.7000000000000001, -1.74), (-0.72, -1.8), (-0.74, -1.9000000000000001), (-0.74, -1.98), (-0.76, -2.04), (-0.78, -2.1), (-0.8, -2.18), (-0.8200000000000001, -2.24), (-0.9, -2.2600000000000002), (-0.96, -2.3000000000000003), (-1.02, -2.32), (-1.08, -2.34), (-1.1400000000000001, -2.36), (-1.2, -2.38), (-1.28, -2.38), (-1.28, -2.46), (-1.28, -2.54), (-1.3, -2.6), (-1.4000000000000001, -2.62), (-1.46, -2.64), (-1.54, -2.64), (-1.6, -2.68), (-1.68, -2.68), (-1.74, -2.7), (-1.8, -2.72), (-1.86, -2.74), (-1.8800000000000001, -2.8000000000000003), (-1.86, -2.86), (-1.8, -2.92), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke1
  3. Point(a) → E
  4. Point(c) → F
  5. Vector(E, F) → u
  6. Translate(stroke1, u) → stroke1'
  7. AttachCopyToView(PolyLine[(-1.74, -2.9), (-1.82, -2.9), (-1.8800000000000001, -2.94), (-1.92, -3), (-1.98, -2.98), (-2, -2.92), (-2, -2.84), (-2.02, -2.7800000000000002), (-2.04, -2.72), (-2.06, -2.66), (-2.08, -2.56), (-2.04, -2.5), (-1.98, -2.46), (-1.94, -2.4), (-1.8800000000000001, -2.36), (-1.8, -2.36), (-1.72, -2.36), (-1.6600000000000001, -2.38), (-1.58, -2.38), (-1.56, -2.3000000000000003), (-1.54, -2.24), (-1.52, -2.18), (-1.5, -2.12), (-1.44, -2.1), (-1.3800000000000001, -2.08), (-1.32, -2.04), (-1.26, -2.02), (-1.22, -1.96), (-1.2, -1.9000000000000001), (-1.16, -1.84), (-1.1400000000000001, -1.76), (-1.1, -1.7), (-1.08, -1.62), (-1.06, -1.56), (-1.04, -1.5), (-1.02, -1.44), (-0.98, -1.3800000000000001), (-0.92, -1.32), (-0.86, -1.28), (-0.78, -1.26), (-0.72, -1.24), (-0.7000000000000001, -1.18), (-0.66, -1.12), (-0.66, -1.04), (-0.66, -0.9400000000000001), (-0.66, -0.86), (-0.68, -0.8), (-0.72, -0.74), (-0.78, -0.72), (-0.84, -0.7000000000000001), (-0.9, -0.68), (-0.96, -0.66), (-1.04, -0.66), (-1.12, -0.66), (-1.2, -0.66), (-1.28, -0.7000000000000001), (-1.34, -0.72), (-1.4000000000000001, -0.76), (-1.48, -0.8200000000000001), (-1.54, -0.88), (-1.56, -0.9400000000000001), (-1.6, -1), (-1.6, -1.08), (-1.56, -1.1400000000000001), (-1.48, -1.1400000000000001), (-1.4000000000000001, -1.1), (-1.36, -1.04), (-1.34, -0.98), (-1.32, -0.92), (-1.32, -1), (-1.3, -1.06), (-1.3, -1.1400000000000001), (-1.3, -1.22), (-1.32, -1.3), (-1.3800000000000001, -1.34), (-1.48, -1.34), (-1.56, -1.34), (-1.6400000000000001, -1.34), (-1.72, -1.34), (-1.8, -1.32), (-1.82, -1.26), (-1.84, -1.2), (-1.86, -1.1400000000000001), (-1.86, -1.06), (-1.8800000000000001, -1), (-1.8800000000000001, -0.92), (-1.86, -0.84), (-1.8, -0.8), (-1.74, -0.76), (-1.68, -0.72), (-1.62, -0.66), (-1.58, -0.6), (-1.52, -0.56), (-1.48, -0.5), (-1.44, -0.42), (-1.4000000000000001, -0.36), (-1.34, -0.32), (-1.26, -0.32), (-1.18, -0.32), (-1.1, -0.32), (-1.02, -0.32), (-0.96, -0.34), (-0.9, -0.36), (-0.8200000000000001, -0.36), (-0.74, -0.36), (-0.66, -0.36), (-0.58, -0.36), (-0.5, -0.36), (-0.42, -0.36), (-0.38, -0.3), (-0.32, -0.24), (-0.26, -0.18), (-0.22, -0.12), (-0.18, -0.02), (-0.14, 0.06), (-0.1, 0.14), (-0.04, 0.18), (0.02, 0.22), (0.1, 0.28), (0.14, 0.34), (0.18, 0.42), (0.2, 0.5), (0.24, 0.6), (0.28, 0.68), (0.34, 0.78), (0.4, 0.86), (0.44, 0.92), (0.48, 1), (0.5, 1.06), (0.52, 1.12), (0.58, 1.16), (0.64, 1.2), (0.7000000000000001, 1.24), (0.78, 1.32), (0.8, 1.3800000000000001), (0.8, 1.46), (0.8, 1.54), (0.78, 1.6), (0.74, 1.6600000000000001), (0.7000000000000001, 1.72), (0.68, 1.78), (0.66, 1.84), (0.66, 1.92), (0.64, 1.98), (0.58, 2), (0.48, 2), (0.42, 1.96), (0.34, 1.96), (0.28, 1.94), (0.22, 1.92), (0.14, 1.92), (0.08, 1.8800000000000001), (0.06, 1.82), (0, 1.78), (-0.04, 1.72), (-0.1, 1.7), (-0.18, 1.68), (-0.24, 1.6600000000000001), (-0.32, 1.68), (-0.38, 1.72), (-0.44, 1.76), (-0.52, 1.76), (-0.6, 1.76), (-0.68, 1.76), (-0.76, 1.76), (-0.8200000000000001, 1.72), (-0.88, 1.7), (-0.96, 1.7), (-1.02, 1.68), (-1.08, 1.6600000000000001), (-1.1400000000000001, 1.6400000000000001), (-1.2, 1.6), (-1.28, 1.6), (-1.36, 1.6), (-1.44, 1.6), (-1.52, 1.6), (-1.6, 1.6), (-1.68, 1.6), (-1.72, 1.6600000000000001), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke2
  8. Point(d) → G
  9. Point(b) → H
  10. Vector(G, H) → v
  11. Translate(stroke2, v) → stroke2'
  12. Point(stroke1') → J
  13. Point(stroke1') → L
  14. Point(stroke1') → M
  15. Point(stroke1') → N
  16. Point(stroke1') → O
  17. Point(stroke1') → P
  18. Point(stroke1') → Q
  19. Point(stroke1') → R
  20. Point(stroke1') → S
  21. Point(stroke1') → T
  22. Point(stroke1') → U
  23. Point(stroke1') → V
  24. Point(stroke1') → W
  25. Point(stroke1') → Z
  26. Point(stroke1') → A_1
  27. Point(stroke1') → B_1
  28. Point(stroke1') → C_1
  29. Point(stroke1') → D_1
  30. Point(stroke1') → E_1
  31. Point(stroke2') → F_1
  32. Point(stroke2') → G_1
  33. Point(stroke2') → H_1
  34. Point(stroke2') → I_1
  35. Point(stroke2') → J_1
  36. Point(stroke2') → K_1
  37. Point(stroke2') → L_1
  38. Point(stroke2') → M_1
  39. Point(stroke2') → N_1
  40. Point(stroke2') → O_1
  41. Point(stroke2') → P_1
  42. Point(stroke2') → Q_1
  43. Point(stroke2') → R_1
  44. Point(stroke2') → S_1
  45. Point(stroke2') → T_1
  46. Point(stroke2') → U_1
  47. Point(stroke2') → V_1
  48. Point(stroke2') → W_1
  49. Point(stroke2') → Z_1
  50. Point(stroke2') → A_2
  51. Point(stroke2') → B_2
  52. Point(stroke2') → D_2
  53. Point(stroke2') → E_2
  54. Point(stroke1) → F_2
  55. Point(stroke1) → G_2
  56. Point(stroke1) → H_2
  57. Point(stroke1) → I_2
  58. Point(stroke1) → J_2
  59. Point(stroke1) → K_2
  60. Point(stroke1) → L_2
  61. Point(stroke1) → M_2
  62. Point(stroke1) → N_2
  63. Point(stroke1) → O_2
  64. Point(stroke1) → Q_2
  65. Point(stroke1) → T_2
  66. Point(stroke1) → U_2
  67. Point(stroke1) → V_2
  68. Point(stroke1) → Z_2
  69. Point(stroke1) → A_3
  70. Point(stroke2) → C_3
  71. Point(stroke2) → D_3
  72. Point(stroke2) → F_3
  73. Point(stroke2) → G_3
  74. Point(stroke2) → H_3
  75. Point(stroke2) → I_3
  76. Point(stroke2) → J_3
  77. Point(stroke2) → K_3
  78. Point(stroke2) → L_3
  79. Point(stroke2) → M_3
  80. Point(stroke2) → N_3
  81. Point(stroke2) → O_3
  82. Point(stroke2) → P_3
  83. Point(stroke2) → Q_3
  84. Point(stroke2) → R_3
  85. Point(stroke2) → S_3
  86. Point(stroke2) → T_3
  87. Point(stroke2) → U_3
  88. Point(stroke2) → V_3
  89. Point(stroke2) → W_3
  90. Polygon(D, I, R, S, T, U, V, W, Z, A_1, B_1, C_1, J, D_1, E_1, C, F_1, G_1, H_1, I_1, J_1, K_1, L_1, K, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, L, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, M, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, N, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, A, C_3, O, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, P, N_3, O_3, P_3, Q_3, R_3, S_3, T_3, F, U_3, V_3, Q, W_3) → poly2, d_1, q, r, s, t, u_1, v_1, w, z, a_1, b_1, i, c_1, d_2, e_1, c_2, f_1, g_1, h_1, i_1, j_1, k_1, j, l_1, m_1, n_1, o_1, p_1, q_1, r_1, s_1, t_1, u_2, k, v_2, w_1, z_1, a_2, b_2, c_3, d_3, e_2, f_2, g_2, l, h_2, i_2, j_2, k_2, l_2, m_2, n_2, o_2, p_2, q_2, m, r_2, s_2, t_2, u_3, v_3, w_2, z_2, a_3, b_3, a_4, n, c_4, d_4, e_3, f_3, g_3, h_3, i_3, j_3, k_3, l_3, o, m_3, n_3, o_3, p_3, q_3, r_3, s_3, t_3, f, u_4, p, v_4, w_3

AI Drawing Prompt Reference

Create a tessellation by translation. Start by drawing a quadrilateral, then translate it along a vector. Draw another quadrilateral and translate it along another vector. Finally, repeatedly translate the translated quadrilaterals to form a complete tessellation pattern.
The prompt above was compiled from the original drawing commands and is for reference only.