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Translation Tessellation 5

Translation Tessellation 5
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2013-07-20 05:20
PolygonVectorTransformation
In collections Translation Tessellation
This example demonstrates the application of translation in tessellation patterns. Key mathematical concepts include translation, polygons, and symmetry. Using GeoGebra commands such as Polygon, Segment, and Translate, one can construct beautiful tessellation patterns. Suitable for middle school and above students to learn geometric transformations and tessellations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, a, F, b, c, d, e, f, C, D, E
  2. Segment(C, G) → g
  3. Segment(G, H) → h
  4. Segment(H, I) → i
  5. Segment(I, J) → j
  6. Segment(J, K) → k
  7. Segment(K, L) → l
  8. Segment(L, M) → m
  9. Segment(M, N) → n
  10. LineBisector(c) → p
  11. Segment(N, O) → q
  12. Segment(O, P) → r
  13. Segment(P, Q) → s
  14. Segment(Q, R) → t
  15. Point(p) → S
  16. Segment(R, S) → a_1
  17. Mirror(C, p) → C'
  18. Mirror(G, p) → G'
  19. Segment(C', G') → g'
  20. Mirror(G, p) → G'_1
  21. Mirror(H, p) → H'
  22. Segment(G'_1, H') → h'
  23. Mirror(H, p) → H'_1
  24. Mirror(I, p) → I'
  25. Segment(H'_1, I') → i'
  26. Mirror(I, p) → I'_1
  27. Mirror(J, p) → J'
  28. Segment(I'_1, J') → j'
  29. Mirror(J, p) → J'_1
  30. Mirror(K, p) → K'
  31. Segment(J'_1, K') → k'
  32. Mirror(K, p) → K'_1
  33. Mirror(L, p) → L'
  34. Segment(K'_1, L') → l'
  35. Mirror(L, p) → L'_1
  36. Mirror(M, p) → M'
  37. Segment(L'_1, M') → m'
  38. Mirror(M, p) → M'_1
  39. Mirror(N, p) → N'
  40. Segment(M'_1, N') → n'
  41. Mirror(N, p) → N'_1
  42. Mirror(O, p) → O'
  43. Segment(N'_1, O') → q'
  44. Mirror(O, p) → O'_1
  45. Mirror(P, p) → P'
  46. Segment(O'_1, P') → r'
  47. Mirror(P, p) → P'_1
  48. Mirror(Q, p) → Q'
  49. Segment(P'_1, Q') → s'
  50. Mirror(Q, p) → Q'_1
  51. Mirror(R, p) → R'
  52. Segment(Q'_1, R') → t'
  53. Mirror(R, p) → R'_1
  54. Mirror(S, p) → S'
  55. Segment(R'_1, S') → b_1
  56. Vector(C, A) → u
  57. Translate(C, u) → C'_1
  58. Translate(D, u) → D'
  59. Segment(C'_1, D') → c'
  60. Translate(C, u) → C'_2
  61. Translate(G, u) → G'_2
  62. Segment(C'_2, G'_2) → g'_1
  63. Translate(G, u) → G'_3
  64. Translate(H, u) → H'_2
  65. Segment(G'_3, H'_2) → h'_1
  66. Translate(H, u) → H'_3
  67. Translate(I, u) → I'_2
  68. Segment(H'_3, I'_2) → i'_1
  69. Translate(I, u) → I'_3
  70. Translate(J, u) → J'_2
  71. Segment(I'_3, J'_2) → j'_1
  72. Translate(J, u) → J'_3
  73. Translate(K, u) → K'_2
  74. Segment(J'_3, K'_2) → k'_1
  75. Translate(K, u) → K'_3
  76. Translate(L, u) → L'_2
  77. Segment(K'_3, L'_2) → l'_1
  78. Translate(L, u) → L'_3
  79. Translate(M, u) → M'_2
  80. Segment(L'_3, M'_2) → m'_1
  81. Translate(M, u) → M'_3
  82. Translate(N, u) → N'_2
  83. Segment(M'_3, N'_2) → n'_1
  84. Translate(N, u) → N'_3
  85. Translate(O, u) → O'_2
  86. Segment(N'_3, O'_2) → q'_1
  87. Translate(O, u) → O'_3
  88. Translate(P, u) → P'_2
  89. Segment(O'_3, P'_2) → r'_1
  90. Translate(P, u) → P'_3
  91. Translate(Q, u) → Q'_2
  92. Segment(P'_3, Q'_2) → s'_1
  93. Translate(Q, u) → Q'_3
  94. Translate(R, u) → R'_2
  95. Segment(Q'_3, R'_2) → t'_1
  96. Translate(R, u) → R'_3
  97. Translate(S, u) → S'_1
  98. Segment(R'_3, S'_1) → c_1
  99. Translate(C', u) → C''
  100. Translate(G', u) → G''
  101. Segment(C'', G'') → g''
  102. Translate(G'_1, u) → T
  103. Translate(H', u) → H''
  104. Segment(T, H'') → h''
  105. Translate(H'_1, u) → U
  106. Translate(I', u) → I''
  107. Segment(U, I'') → i''
  108. Translate(I'_1, u) → V
  109. Translate(J', u) → J''
  110. Segment(V, J'') → j''
  111. Translate(J'_1, u) → W
  112. Translate(K', u) → K''
  113. Segment(W, K'') → k''
  114. Translate(K'_1, u) → Z
  115. Translate(L', u) → L''
  116. Segment(Z, L'') → l''
  117. Translate(L'_1, u) → A_1
  118. Translate(M', u) → M''
  119. Segment(A_1, M'') → m''
  120. Translate(M'_1, u) → B_1
  121. Translate(N', u) → N''
  122. Segment(B_1, N'') → n''
  123. Translate(N'_1, u) → C_1
  124. Translate(O', u) → O''
  125. Segment(C_1, O'') → q''
  126. Translate(O'_1, u) → D_1
  127. Translate(P', u) → P''
  128. Segment(D_1, P'') → r''
  129. Translate(P'_1, u) → E_1
  130. Translate(Q', u) → Q''
  131. Segment(E_1, Q'') → s''
  132. Translate(Q'_1, u) → F_1
  133. Translate(R', u) → R''
  134. Segment(F_1, R'') → t''
  135. Translate(R'_1, u) → G_1
  136. Translate(S', u) → S''
  137. Segment(G_1, S'') → d_1
  138. Segment(B, H_1) → e_1
  139. Segment(H_1, I_1) → f_1
  140. Segment(I_1, J_1) → g_1
  141. Segment(J_1, K_1) → h_1
  142. Segment(K_1, L_1) → i_1
  143. Segment(L_1, M_1) → j_1
  144. Segment(M_1, N_1) → k_1
  145. Segment(N_1, O_1) → l_1
  146. Segment(O_1, P_1) → m_1
  147. Segment(P_1, Q_1) → n_1
  148. Segment(Q_1, C) → p_1
  149. Vector(B, F) → v
  150. Translate(B, v) → B'
  151. Translate(C, v) → C'_3
  152. Segment(B', C'_3) → b'
  153. Translate(B, v) → B'_1
  154. Translate(H_1, v) → R_1
  155. Segment(B'_1, R_1) → q_1
  156. Translate(H_1, v) → S_1
  157. Translate(I_1, v) → T_1
  158. Segment(S_1, T_1) → r_1
  159. Translate(I_1, v) → U_1
  160. Translate(J_1, v) → V_1
  161. Segment(U_1, V_1) → s_1
  162. Translate(J_1, v) → W_1
  163. Translate(K_1, v) → Z_1
  164. Segment(W_1, Z_1) → t_1
  165. Translate(K_1, v) → A_2
  166. Translate(L_1, v) → B_2
  167. Segment(A_2, B_2) → a_2
  168. Translate(L_1, v) → C_2
  169. Translate(M_1, v) → D_2
  170. Segment(C_2, D_2) → b_2
  171. Translate(M_1, v) → E_2
  172. Translate(N_1, v) → F_2
  173. Segment(E_2, F_2) → c_2
  174. Translate(N_1, v) → G_2
  175. Translate(O_1, v) → H_2
  176. Segment(G_2, H_2) → d_2
  177. Translate(O_1, v) → I_2
  178. Translate(P_1, v) → J_2
  179. Segment(I_2, J_2) → e_2
  180. Translate(P_1, v) → K_2
  181. Translate(Q_1, v) → L_2
  182. Segment(K_2, L_2) → f_2
  183. Translate(Q_1, v) → M_2
  184. Translate(C, v) → C'_4
  185. Segment(M_2, C'_4) → g_2

AI Drawing Prompt Reference

Draw a hexagon, then use the perpendicular bisector of one of its sides as the axis for mirror transformations to create a hexagon tessellation pattern. First, draw hexagon ABCDEF, then draw the perpendicular bisector p of side CD, and mirror points C and G to get C' and G', and connect C' and G' to get g'. Repeat this process for H, I, J, K, L, M, N, O, P, and Q to generate a series of hexagons and form a tessellation pattern.
The prompt above was compiled from the original drawing commands and is for reference only.