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Translation Tessellation Step 10

Translation Tessellation Step 10
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2014-03-28 10:13
VectorCoordinate GeometryProbability & StatisticsGeometric Construction
In collections Translation Tesselation
This example demonstrates the construction of a translation tessellation through translation operations. Key math concepts include coordinate geometry, vectors, translation transformations, right triangles, and probability & statistics. The construction involves commands and objects like Polygon, Segment, Vector, Translate, Intersect, Point, and Circle as outlined in the summary. Suitable for high school students learning geometric transformations, coordinate geometry, and probability & statistics.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Segment(A, E) → e
  3. Segment(E, F) → f
  4. Segment(F, G) → g
  5. Segment(G, H) → h
  6. Segment(J, B) → k
  7. Segment(H, J) → i
  8. Vector(A, D) → u
  9. Translate(A, u) → A'
  10. Translate(E, u) → E'
  11. Segment(A', E') → e'
  12. Translate(E, u) → E'_1
  13. Translate(F, u) → F'
  14. Segment(E'_1, F') → f'
  15. Translate(F, u) → F'_1
  16. Translate(G, u) → G'
  17. Segment(F'_1, G') → g'
  18. Translate(G, u) → G'_1
  19. Translate(H, u) → H'
  20. Segment(G'_1, H') → h'
  21. Translate(J, u) → J'
  22. Translate(B, u) → B'
  23. Segment(J', B') → k'
  24. Translate(H, u) → H'_1
  25. Translate(J, u) → J'_1
  26. Segment(H'_1, J'_1) → i'
  27. Segment(D, I) → j
  28. Segment(I, K) → l
  29. Segment(K, L) → m
  30. Segment(L, M) → n
  31. Segment(M, N) → p
  32. Segment(N, A) → q
  33. Vector(A, B) → v
  34. Translate(A, v) → A'_1
  35. Translate(E, v) → E'_2
  36. Segment(A'_1, E'_2) → e'_1
  37. Translate(A', v) → A''
  38. Translate(E', v) → E''
  39. Segment(A'', E'') → e''
  40. Translate(D, v) → D'
  41. Translate(I, v) → I'
  42. Segment(D', I') → j'
  43. Translate(I, v) → I'_1
  44. Translate(K, v) → K'
  45. Segment(I'_1, K') → l'
  46. Translate(K, v) → K'_1
  47. Translate(L, v) → L'
  48. Segment(K'_1, L') → m'
  49. Translate(L, v) → L'_1
  50. Translate(M, v) → M'
  51. Segment(L'_1, M') → n'
  52. Translate(M, v) → M'_1
  53. Translate(N, v) → N'
  54. Segment(M'_1, N') → p'
  55. Translate(N, v) → N'_1
  56. Translate(A, v) → A'_2
  57. Segment(N'_1, A'_2) → q'
  58. Intersect(f, g) → O
  59. Intersect(g, h) → P
  60. Point(i) → Q
  61. Intersect(k, i) → R
  62. Intersect(p', q') → S
  63. Intersect(n', p') → T
  64. Intersect(m', n') → U
  65. Intersect(l', m') → V
  66. Intersect(j', l') → W
  67. Intersect(k', i') → Z
  68. Intersect(h', i') → A_1
  69. Intersect(g', h') → B_1
  70. Intersect(f', g') → C_1
  71. Point(l) → D_1
  72. Intersect(l, m) → E_1
  73. Intersect(m, n) → F_1
  74. Intersect(n, p) → G_1
  75. Intersect(p, q) → H_1
  76. Polygon(A, O, W, C, Z, A_1, B_1, C_1, D, D_1, E_1, F_1, P, G_1, H_1, Q, R, B, S, T, U, V) → poly2, a_1, v_1, w, c_1, z, a_2, b_2, c_2, d_1, d_2, e_1, o, f_1, g_1, h_1, p_1, q_1, r, b_1, s, t, u_1
  77. Circle(I_1, J_1) → k_1
  78. Intersect(n', p') → K_1
  79. Intersect(m', n') → L_1
  80. Point(m') → M_1
  81. Point(n') → N_1
  82. Point(n') → P_1
  83. Point(n') → R_1
  84. Polygon(K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1) → poly3, k_2, l_1, m_1, n_1, o_1, p_2, q_2, r_1, s_1
  85. Intersect(n, p) → T_1
  86. Intersect(m, n) → U_1
  87. Polygon(T_1, U_1, V_1, W_1, Z_1, A_2, B_2) → poly4, t_1, u_2, v_2, w_1, z_1, a_3, b_3
  88. Translate(A, v) → A'_3
  89. Translate(O, v) → O'
  90. Translate(P, v) → P'
  91. Translate(Q, v) → Q'
  92. Translate(R, v) → R'
  93. Translate(B, v) → B'_1
  94. Translate(S, v) → S'
  95. Translate(T, v) → T'
  96. Translate(U, v) → U'
  97. Translate(V, v) → V'
  98. Translate(W, v) → W'
  99. Translate(C, v) → C'
  100. Translate(Z, v) → Z'
  101. Translate(A_1, v) → C_2
  102. Translate(B_1, v) → D_2
  103. Translate(C_1, v) → E_2
  104. Translate(D, v) → D'_1
  105. Translate(D_1, v) → F_2
  106. Translate(E_1, v) → G_2
  107. Translate(F_1, v) → H_2
  108. Translate(G_1, v) → I_2
  109. Translate(H_1, v) → J_2
  110. Polygon(A'_3, O', W', C', Z', C_2, D_2, E_2, D'_1, F_2, G_2, H_2, P', I_2, J_2, Q', R', B'_1, S', T', U', V') → poly2', a'_3, v', w', c', z', c_3, d_3, e_2, d'_1, f_2, g_2, o', h_2, i_2, j_2, p'_1, q'_1, r', b'_1, s', t', u'
  111. Translate(K_1, v) → K_2
  112. Translate(L_1, v) → L_2
  113. Translate(M_1, v) → M_2
  114. Translate(N_1, v) → N_2
  115. Translate(O_1, v) → O_2
  116. Translate(P_1, v) → P_2
  117. Translate(Q_1, v) → Q_2
  118. Translate(R_1, v) → R_2
  119. Translate(S_1, v) → S_2
  120. Polygon(K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2) → poly3', k_3, l_2, m_2, n_2, o_2, p_3, q_3, r_2, s_2
  121. Translate(T_1, v) → T_2
  122. Translate(U_1, v) → U_2
  123. Translate(V_1, v) → V_2
  124. Translate(W_1, v) → W_2
  125. Translate(Z_1, v) → Z_2
  126. Translate(A_2, v) → A_3
  127. Translate(B_2, v) → B_3
  128. Polygon(T_2, U_2, V_2, W_2, Z_2, A_3, B_3) → poly4', t_2, u_3, v_3, w_2, z_2, a_4, b_4
  129. Translate(k_1, v) → e_3
  130. Translate(A, v) → A'_4
  131. Translate(E, v) → E'_3
  132. Segment(A'_4, E'_3) → e'_2
  133. Translate(E, v) → E'_4
  134. Translate(F, v) → F'_2
  135. Segment(E'_4, F'_2) → f'_1
  136. Translate(F, v) → F'_3
  137. Translate(G, v) → G'_2
  138. Segment(F'_3, G'_2) → g'_1
  139. Translate(G, v) → G'_3
  140. Translate(H, v) → H'_2
  141. Segment(G'_3, H'_2) → h'_1
  142. Translate(J, v) → J'_2
  143. Translate(B, v) → B'_2
  144. Segment(J'_2, B'_2) → k'_1
  145. Translate(H, v) → H'_3
  146. Translate(J, v) → J'_3
  147. Segment(H'_3, J'_3) → i'_1
  148. Translate(A', v) → A''_1
  149. Translate(E', v) → E''_1
  150. Segment(A''_1, E''_1) → e''_1
  151. Translate(E'_1, v) → C_3
  152. Translate(F', v) → F''
  153. Segment(C_3, F'') → f''
  154. Translate(F'_1, v) → D_3
  155. Translate(G', v) → G''
  156. Segment(D_3, G'') → g''
  157. Translate(G'_1, v) → E_3
  158. Translate(H', v) → H''
  159. Segment(E_3, H'') → h''
  160. Translate(J', v) → J''
  161. Translate(B', v) → B''
  162. Segment(J'', B'') → k''
  163. Translate(H'_1, v) → F_3
  164. Translate(J'_1, v) → G_3
  165. Segment(F_3, G_3) → i''
  166. Translate(D, v) → D'_2
  167. Translate(I, v) → I'_2
  168. Segment(D'_2, I'_2) → j'_1
  169. Translate(I, v) → I'_3
  170. Translate(K, v) → K'_2
  171. Segment(I'_3, K'_2) → l'_1
  172. Translate(K, v) → K'_3
  173. Translate(L, v) → L'_2
  174. Segment(K'_3, L'_2) → m'_1
  175. Translate(L, v) → L'_3
  176. Translate(M, v) → M'_2
  177. Segment(L'_3, M'_2) → n'_1
  178. Translate(M, v) → M'_3
  179. Translate(N, v) → N'_2
  180. Segment(M'_3, N'_2) → p'_2
  181. Translate(N, v) → N'_3
  182. Translate(A, v) → A'_5
  183. Segment(N'_3, A'_5) → q'_2
  184. Translate(D', v) → D''
  185. Translate(I', v) → I''
  186. Segment(D'', I'') → j''
  187. Translate(I'_1, v) → H_3
  188. Translate(K', v) → K''
  189. Segment(H_3, K'') → l''
  190. Translate(K'_1, v) → I_3
  191. Translate(L', v) → L''
  192. Segment(I_3, L'') → m''
  193. Translate(L'_1, v) → J_3
  194. Translate(M', v) → M''
  195. Segment(J_3, M'') → n''
  196. Translate(M'_1, v) → K_3
  197. Translate(N', v) → N''
  198. Segment(K_3, N'') → p''
  199. Translate(N'_1, v) → L_3
  200. Translate(A'_2, v) → M_3
  201. Segment(L_3, M_3) → q''
  202. Translate(I_1, v) → N_3