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Translation Tessellation 6

Translation Tessellation 6
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2013-07-20 05:21
PolygonVectorTransformation
In collections Translation Tessellation
This example demonstrates the application of translation transformation in geometric construction. By using translation vectors, a series of parallelograms are generated, forming a tessellation. Key mathematical concepts include translation, vectors, and polygons. The construction uses GeoGebra commands such as Polygon, Segment, Vector, and Translate. Suitable for middle school and above students to learn about 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
  186. Mirror(B, p) → B'_2
  187. Mirror(C, p) → C'_5
  188. Segment(B'_2, C'_5) → b'_1
  189. Mirror(B, p) → B'_3
  190. Mirror(H_1, p) → N_2
  191. Segment(B'_3, N_2) → h_2
  192. Mirror(H_1, p) → O_2
  193. Mirror(I_1, p) → P_2
  194. Segment(O_2, P_2) → i_2
  195. Mirror(I_1, p) → Q_2
  196. Mirror(J_1, p) → R_2
  197. Segment(Q_2, R_2) → j_2
  198. Mirror(J_1, p) → S_2
  199. Mirror(K_1, p) → T_2
  200. Segment(S_2, T_2) → k_2
  201. Mirror(K_1, p) → U_2
  202. Mirror(L_1, p) → V_2
  203. Segment(U_2, V_2) → l_2
  204. Mirror(L_1, p) → W_2
  205. Mirror(M_1, p) → Z_2
  206. Segment(W_2, Z_2) → m_2
  207. Mirror(M_1, p) → A_3
  208. Mirror(N_1, p) → B_3
  209. Segment(A_3, B_3) → n_2
  210. Mirror(N_1, p) → C_3
  211. Mirror(O_1, p) → D_3
  212. Segment(C_3, D_3) → p_2
  213. Mirror(O_1, p) → E_3
  214. Mirror(P_1, p) → F_3
  215. Segment(E_3, F_3) → q_2
  216. Mirror(P_1, p) → G_3
  217. Mirror(Q_1, p) → H_3
  218. Segment(G_3, H_3) → r_2
  219. Mirror(Q_1, p) → I_3
  220. Mirror(C, p) → C'_6
  221. Segment(I_3, C'_6) → s_2

AI Drawing Prompt Reference

Draw a hexagon and generate a series of parallelograms using translation vectors to form a tessellation. Start by sketching the hexagon, then draw segments from its vertices. Find the perpendicular bisectors of these segments and mark their intersections. Mirror the vertices of the hexagon across these bisectors, connect the corresponding points to create parallelograms, and observe the resulting pattern of translations.
The prompt above was compiled from the original drawing commands and is for reference only.