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Translation Tessellation Example by BenPerryRM

Translation Tessellation Example by BenPerryRM
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2013-07-20 05:23
PolygonTransformationGeometric Construction
In collections Translation Tessellation
This example demonstrates the creation of a geometric tessellation pattern through translation operations. It involves core mathematical concepts such as translation transformation, polygon construction, and coordinate geometry. Key GeoGebra commands used include Polygon, Segment, LineBisector, Point, Mirror, Vector, and Translate for constructing and manipulating the shapes. It is suitable for high school mathematics education, helping students understand geometric transformations and the generation of fractal patterns.

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
  222. Vector(E, A) → w
  223. Translate(D, w) → D'_1
  224. Translate(E, w) → E'
  225. Segment(D'_1, E') → d'
  226. Translate(B'_2, w) → J_3
  227. Translate(C'_5, w) → K_3
  228. Segment(J_3, K_3) → t_2
  229. Translate(B'_3, w) → L_3
  230. Translate(N_2, w) → M_3
  231. Segment(L_3, M_3) → a_3
  232. Translate(O_2, w) → N_3
  233. Translate(P_2, w) → O_3
  234. Segment(N_3, O_3) → b_3
  235. Translate(Q_2, w) → P_3
  236. Translate(R_2, w) → Q_3
  237. Segment(P_3, Q_3) → c_3
  238. Translate(S_2, w) → R_3
  239. Translate(T_2, w) → S_3
  240. Segment(R_3, S_3) → d_3
  241. Translate(U_2, w) → T_3
  242. Translate(V_2, w) → U_3
  243. Segment(T_3, U_3) → e_3
  244. Translate(W_2, w) → V_3
  245. Translate(Z_2, w) → W_3
  246. Segment(V_3, W_3) → f_3
  247. Translate(A_3, w) → Z_3
  248. Translate(B_3, w) → A_4
  249. Segment(Z_3, A_4) → g_3
  250. Translate(C_3, w) → B_4
  251. Translate(D_3, w) → C_4
  252. Segment(B_4, C_4) → h_3
  253. Translate(E_3, w) → D_4
  254. Translate(F_3, w) → E_4
  255. Segment(D_4, E_4) → i_3
  256. Translate(G_3, w) → F_4
  257. Translate(H_3, w) → G_4
  258. Segment(F_4, G_4) → j_3
  259. Translate(I_3, w) → H_4
  260. Translate(C'_6, w) → I_4
  261. Segment(H_4, I_4) → k_3
  262. Translate(C', w) → C''_1
  263. Translate(C'_3, w) → J_4
  264. Translate(C'_4, w) → K_4

AI Drawing Prompt Reference

Draw a hexagon and connect one of its vertices to the midpoint of the opposite side to form a line segment. Reflect the hexagon over this line segment to create a mirrored shape. Repeat this reflection for each vertex of the hexagon to generate a tessellation pattern composed of multiple hexagons, demonstrating translation and reflection transformations.
The prompt above was compiled from the original drawing commands and is for reference only.