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Tessellation by Translation by jahatch8 (3)

Tessellation by Translation by jahatch8 (3)
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2014-03-30 05:26
PolygonVectorTransformation
In collections Tesselation by Translation Tesselation by Translation
This example demonstrates the process of creating a tessellation through translation. Key mathematical concepts include translation transformation and polygons. Using GeoGebra commands such as Polygon and Translate, a tessellation can be created. 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[(2.74, -3.06), (2.68, -3.08), (2.62, -3.14), (2.56, -3.2), (2.52, -3.2600000000000002), (2.46, -3.2800000000000002), (2.38, -3.34), (2.32, -3.38), (2.2600000000000002, -3.44), (2.22, -3.5), (2.18, -3.56), (2.08, -3.56), (1.98, -3.56), (1.8800000000000001, -3.56), (1.82, -3.54), (1.76, -3.52), (1.6600000000000001, -3.48), (1.6, -3.46), (1.54, -3.44), (1.46, -3.44), (1.3800000000000001, -3.46), (1.32, -3.5), (1.26, -3.54), (1.24, -3.6), (1.16, -3.66), (1.1, -3.74), (1.04, -3.8200000000000003), (0.98, -3.86), (0.96, -3.8000000000000003), (0.92, -3.72), (0.9, -3.66), (0.84, -3.6), (0.9, -3.54), (0.96, -3.46), (1.02, -3.44), (1.04, -3.38), (1.1, -3.34), (1.16, -3.3000000000000003), (1.22, -3.24), (1.26, -3.18), (1.32, -3.12), (1.3800000000000001, -3.1), (1.3800000000000001, -3.02), (1.36, -2.96), (1.32, -2.9), (1.26, -2.84), (1.2, -2.7800000000000002), (1.16, -2.72), (1.1, -2.7), (1.04, -2.64), (0.98, -2.58), (0.92, -2.52), (0.86, -2.44), (0.8, -2.36), (0.74, -2.32), (0.68, -2.24), (0.62, -2.18), (0.56, -2.1), (0.5, -2.02), (0.46, -1.96), (0.42, -1.9000000000000001), (0.38, -1.84), (0.34, -1.78), (0.28, -1.8), (0.22, -1.82), (0.14, -1.84), (0.06, -1.8800000000000001), (0, -1.9000000000000001), (-0.08, -1.94), (-0.12, -2), (-0.2, -2.04), (-0.28, -2.06), (-0.36, -2.06), (-0.42, -2.08), (-0.48, -2.1), (-0.56, -2.14), (-0.62, -2.16), (-0.68, -2.18), (-0.78, -2.18), (-0.86, -2.18), (-0.9400000000000001, -2.18), (-0.98, -2.24), (-0.98, -2.32), (-0.98, -2.4), (-1, -2.48), (-1.06, -2.5), (-1.12, -2.52), (-1.18, -2.56), (-1.24, -2.6), (-1.3, -2.62), (-1.32, -2.68), (-1.3800000000000001, -2.72), (-1.4000000000000001, -2.7800000000000002), (-1.44, -2.84), (-1.5, -2.88), (-1.46, -2.94), (-1.4000000000000001, -2.98), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke1
  3. Point(a) → E
  4. Vector(E, F) → u
  5. Translate(stroke1, u) → stroke1'
  6. AttachCopyToView(PolyLine[(-1.3800000000000001, -2.98), (-1.46, -3), (-1.52, -3.02), (-1.58, -3.04), (-1.6600000000000001, -3.04), (-1.68, -2.98), (-1.68, -2.88), (-1.7, -2.82), (-1.68, -2.72), (-1.6400000000000001, -2.66), (-1.6, -2.6), (-1.54, -2.56), (-1.5, -2.5), (-1.48, -2.44), (-1.44, -2.36), (-1.4000000000000001, -2.3000000000000003), (-1.36, -2.2), (-1.36, -2.12), (-1.34, -2), (-1.3, -1.94), (-1.24, -1.92), (-1.18, -1.9000000000000001), (-1.12, -1.86), (-1.06, -1.82), (-1, -1.8), (-0.9400000000000001, -1.78), (-0.86, -1.76), (-0.8, -1.74), (-0.72, -1.68), (-0.66, -1.6400000000000001), (-0.6, -1.58), (-0.58, -1.52), (-0.58, -1.44), (-0.58, -1.36), (-0.58, -1.28), (-0.6, -1.18), (-0.62, -1.12), (-0.64, -1.06), (-0.7000000000000001, -1.04), (-0.76, -1.06), (-0.84, -1.08), (-0.92, -1.08), (-1, -1.08), (-1.06, -1.1), (-1.12, -1.12), (-1.2, -1.12), (-1.28, -1.12), (-1.36, -1.12), (-1.44, -1.12), (-1.5, -1.1400000000000001), (-1.44, -1.16), (-1.36, -1.16), (-1.3, -1.2), (-1.22, -1.2), (-1.18, -1.26), (-1.12, -1.3), (-1.1, -1.36), (-1.02, -1.36), (-0.96, -1.3800000000000001), (-0.9400000000000001, -1.44), (-0.96, -1.52), (-1.02, -1.56), (-1.1, -1.56), (-1.2, -1.56), (-1.28, -1.56), (-1.36, -1.56), (-1.42, -1.54), (-1.48, -1.52), (-1.54, -1.5), (-1.62, -1.5), (-1.68, -1.48), (-1.74, -1.46), (-1.78, -1.4000000000000001), (-1.8, -1.34), (-1.82, -1.28), (-1.82, -1.2), (-1.8, -1.1400000000000001), (-1.78, -1.06), (-1.76, -1), (-1.76, -0.92), (-1.7, -0.9), (-1.6400000000000001, -0.88), (-1.56, -0.88), (-1.48, -0.88), (-1.42, -0.8200000000000001), (-1.34, -0.78), (-1.28, -0.74), (-1.2, -0.7000000000000001), (-1.1400000000000001, -0.66), (-1.08, -0.6), (-1.02, -0.58), (-0.96, -0.56), (-0.9, -0.52), (-0.8200000000000001, -0.52), (-0.76, -0.48), (-0.72, -0.42), (-0.66, -0.4), (-0.6, -0.38), (-0.54, -0.32), (-0.5, -0.26), (-0.48, -0.2), (-0.46, -0.14), (-0.46, -0.04), (-0.44, 0.04), (-0.4, 0.14), (-0.36, 0.24), (-0.34, 0.3), (-0.28, 0.36), (-0.22, 0.42), (-0.16, 0.48), (-0.1, 0.5), (-0.04, 0.54), (0.02, 0.62), (0.08, 0.7000000000000001), (0.12, 0.78), (0.14, 0.84), (0.12, 0.92), (0.1, 0.98), (0.08, 1.04), (0.06, 1.1), (0.04, 1.16), (0.04, 1.24), (0.04, 1.32), (0.02, 1.3800000000000001), (0.02, 1.46), (-0.04, 1.42), (-0.06, 1.36), (-0.12, 1.3), (-0.2, 1.26), (-0.26, 1.22), (-0.32, 1.2), (-0.4, 1.2), (-0.48, 1.2), (-0.56, 1.2), (-0.64, 1.2), (-0.7000000000000001, 1.1400000000000001), (-0.76, 1.12), (-0.8200000000000001, 1.08), (-0.9, 1.08), (-0.98, 1.08), (-1.06, 1.08), (-1.1400000000000001, 1.08), (-1.22, 1.08), (-1.3, 1.08), (-1.36, 1.04), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke2
  7. Point(d) → G
  8. Point(b) → H
  9. Vector(G, H) → v
  10. Translate(stroke2, v) → stroke2'
  11. Point(stroke1') → J
  12. Point(stroke1') → K
  13. Point(stroke1') → M
  14. Point(stroke1') → N
  15. Point(stroke1') → O
  16. Point(stroke1') → P
  17. Point(stroke1') → Q
  18. Point(stroke1') → S
  19. Point(stroke1') → T
  20. Point(stroke1') → U
  21. Point(stroke2') → V
  22. Point(stroke2') → W
  23. Point(stroke2') → A_1
  24. Point(stroke2') → B_1
  25. Point(stroke2') → C_1
  26. Point(stroke2') → D_1
  27. Point(stroke2') → F_1
  28. Point(stroke2') → G_1
  29. Point(stroke2') → H_1
  30. Point(stroke2') → I_1
  31. Point(stroke2') → J_1
  32. Point(stroke2') → K_1
  33. Point(stroke2') → L_1
  34. Point(stroke2') → M_1
  35. Point(stroke1) → N_1
  36. Point(stroke1) → O_1
  37. Point(stroke1) → P_1
  38. Point(stroke1) → Q_1
  39. Point(stroke1) → S_1
  40. Point(stroke1) → T_1
  41. Point(stroke1) → U_1
  42. Point(stroke1) → V_1
  43. Point(stroke2) → W_1
  44. Point(stroke2) → Z_1
  45. Point(stroke2) → A_2
  46. Point(stroke2) → B_2
  47. Point(stroke2) → C_2
  48. Point(stroke2) → D_2
  49. Point(stroke2) → E_2
  50. Point(stroke2) → F_2
  51. Point(stroke2) → G_2
  52. Point(stroke2) → H_2
  53. Point(stroke2) → I_2
  54. Point(stroke2) → J_2
  55. Point(stroke2) → K_2
  56. Polygon(D, I, R, S, T, U, C, V, W, Z, A_1, B_1, J, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, K, M_1, B, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, L, V_1, A, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, M, G_2, H_2, I_2, F, J_2, K_2, N, O, P, Q) → poly2, d_1, q, r, s, t, u_1, c_1, v_1, w, z, a_1, i, b_1, c_2, d_2, e_1, f_1, g_1, h_1, i_1, j_1, k_1, j, l_1, m_1, b_2, n_1, o_1, p_1, q_1, r_1, s_1, t_1, k, u_2, v_2, a_2, w_1, z_1, a_3, b_3, c_3, d_3, e_2, l, f_2, g_2, h_2, i_2, f, j_2, k_2, m, n, o, p
  57. Vector(W_1, I) → e
  58. Translate(stroke1, e) → stroke1'_1
  59. Translate(stroke1', e) → stroke1''
  60. Translate(stroke2, e) → stroke2'_1
  61. Translate(stroke2', e) → stroke2''
  62. Translate(D, e) → D'
  63. Translate(I, e) → I'
  64. Translate(J, e) → J'
  65. Translate(K, e) → K'
  66. Translate(L, e) → L'
  67. Translate(M, e) → M'
  68. Translate(N, e) → N'
  69. Translate(O, e) → O'
  70. Translate(P, e) → P'
  71. Translate(Q, e) → Q'
  72. Translate(R, e) → R'
  73. Translate(S, e) → S'
  74. Translate(T, e) → T'
  75. Translate(U, e) → U'
  76. Translate(C, e) → C'
  77. Translate(V, e) → V'
  78. Translate(W, e) → W'
  79. Translate(Z, e) → Z'
  80. Translate(A_1, e) → L_2
  81. Translate(B_1, e) → M_2
  82. Translate(C_1, e) → N_2
  83. Translate(D_1, e) → O_2
  84. Translate(E_1, e) → P_2
  85. Translate(F_1, e) → Q_2
  86. Translate(G_1, e) → R_2
  87. Translate(H_1, e) → S_2
  88. Translate(I_1, e) → T_2
  89. Translate(J_1, e) → U_2
  90. Translate(K_1, e) → V_2
  91. Translate(L_1, e) → W_2
  92. Translate(M_1, e) → Z_2
  93. Translate(B, e) → B'
  94. Translate(N_1, e) → A_3
  95. Translate(O_1, e) → B_3
  96. Translate(P_1, e) → C_3
  97. Translate(Q_1, e) → D_3
  98. Translate(R_1, e) → E_3
  99. Translate(S_1, e) → F_3
  100. Translate(T_1, e) → G_3
  101. Translate(U_1, e) → H_3
  102. Translate(V_1, e) → I_3
  103. Translate(A, e) → A'
  104. Translate(W_1, e) → J_3
  105. Translate(Z_1, e) → K_3
  106. Translate(A_2, e) → L_3
  107. Translate(B_2, e) → M_3
  108. Translate(C_2, e) → N_3
  109. Translate(D_2, e) → O_3
  110. Translate(E_2, e) → P_3
  111. Translate(F_2, e) → Q_3
  112. Translate(G_2, e) → R_3
  113. Translate(H_2, e) → S_3
  114. Translate(I_2, e) → T_3
  115. Translate(F, e) → F'
  116. Translate(J_2, e) → U_3
  117. Translate(K_2, e) → V_3
  118. Polygon(D', I', R', S', T', U', C', V', W', Z', L_2, M_2, J', N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, K', Z_2, B', A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, L', I_3, A', J_3, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, M', R_3, S_3, T_3, F', U_3, V_3, N', O', P', Q') → poly2', d', q', r', s', t', u', c', v', w', z', l_2, i', m_2, n_2, o_2, p_2, q_2, r_2, s_2, t_2, u_3, v_3, j', w_2, z_2, b', a_4, b_4, c_4, d_4, e_3, f_3, g_3, k', h_3, i_3, a', j_3, k_3, l_3, m_3, n_3, o_3, p_3, l', q_3, r_3, s_3, t_3, f', u_4, v_4, m', n', o', p'
  119. Translate(E, e) → E'
  120. Translate(G, e) → G'
  121. Translate(H, e) → H'

AI Drawing Prompt Reference

Create a tessellation through translation. First, draw a quadrilateral, then translate it to create a repeated pattern. Use the translated quadrilateral to translate again and form a more complex tessellation. Finally, mark key points from the translated quadrilaterals, such as J, K, M, N, etc.
The prompt above was compiled from the original drawing commands and is for reference only.