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Translation by Vector & Parallelograms Tessellations

Translation by Vector & Parallelograms Tessellations
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2014-11-22 15:51
PolygonVectorCoordinate GeometryTransformationGeometric Construction
This example demonstrates geometric tessellations constructed using translation vectors and parallelograms. It involves core math concepts like translation, vector, parallelogram, set theory, ratios, differential calculus, subtraction, and confidence intervals. The construction utilizes GeoGebra commands such as Segment, Line, Intersect, Polygon, Translate, and Vector. Suitable for high school mathematics education to understand spatial transformations and geometric figure composition.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Line(C, a) → b
  3. Segment(A, C) → c
  4. Line(B, c) → d
  5. Intersect(b, d) → D
  6. Segment(C, D) → e
  7. Segment(B, D) → f
  8. Polygon(A, C, E) → poly1, e_1, a_1, c_1
  9. Polygon(A, C, D, B) → poly2, a_2, c_2, d_1, b_1
  10. Translate(A, u) → A'
  11. Translate(C, u) → C'
  12. Translate(E, u) → E'
  13. Polygon(A', C', E') → poly1', e', a', c'
  14. Vector(C, D) → v
  15. Translate(A, v) → A'_1
  16. Translate(C, v) → C'_1
  17. Translate(E, v) → E'_1
  18. Polygon(A'_1, C'_1, E'_1) → poly1'_1, e'_1, a'_1, c'_1
  19. Polygon(C, F, D) → poly3, d_2, c_3, f_1
  20. Translate(C, w) → C'_2
  21. Translate(F, w) → F'
  22. Translate(D, w) → D'
  23. Polygon(C'_2, F', D') → poly3', d', c'_2, f'
  24. Vector(C, A) → g
  25. Translate(C, g) → C'_3
  26. Translate(F, g) → F'_1
  27. Translate(D, g) → D'_1
  28. Polygon(C'_3, F'_1, D'_1) → poly3'_1, d'_1, c'_3, f'_1
  29. Polygon(B, F'_1, A, E, C, F, D, E'_1) → poly4, b_2, f'_2, a_3, e_2, c_4, f_2, d_3, e'_2
  30. Vector(C, A) → h
  31. Translate(B, h) → B'
  32. Translate(F'_1, h) → G
  33. Translate(A, h) → A'_2
  34. Translate(E, h) → E'_2
  35. Translate(C, h) → C'_4
  36. Translate(F, h) → F'_2
  37. Translate(D, h) → D'_2
  38. Translate(E'_1, h) → H
  39. Polygon(B', G, A'_2, E'_2, C'_4, F'_2, D'_2, H) → poly4', b', g_1, a'_2, e'_3, c'_4, f'_3, d'_2, h_1
  40. Vector(A, A'_2) → i
  41. Translate(B', i) → B''
  42. Translate(G, i) → G'
  43. Translate(A'_2, i) → I
  44. Translate(E'_2, i) → J
  45. Translate(C'_4, i) → K
  46. Translate(F'_2, i) → L
  47. Translate(D'_2, i) → M
  48. Translate(H, i) → H'
  49. Polygon(B'', G', I, J, K, L, M, H') → poly4'', b'', g', i_1, j, k, l, m, h'
  50. Vector(E'_2, H) → n
  51. Translate(B', n) → B''_1
  52. Translate(G, n) → G'_1
  53. Translate(A'_2, n) → N
  54. Translate(E'_2, n) → O
  55. Translate(C'_4, n) → P
  56. Translate(F'_2, n) → Q
  57. Translate(D'_2, n) → R
  58. Translate(H, n) → H'_1
  59. Polygon(B''_1, G'_1, N, O, P, Q, R, H'_1) → poly4''_1, b''_1, g'_1, n_1, o, p, q, r, h'_1
  60. Vector(E, E'_1) → s
  61. Translate(B, s) → B'_1
  62. Translate(F'_1, s) → S
  63. Translate(A, s) → A'_3
  64. Translate(E, s) → E'_3
  65. Translate(C, s) → C'_5
  66. Translate(F, s) → F'_3
  67. Translate(D, s) → D'_3
  68. Translate(E'_1, s) → T
  69. Polygon(B'_1, S, A'_3, E'_3, C'_5, F'_3, D'_3, T) → poly4'_1, b'_1, s_1, a'_3, e'_4, c'_5, f'_4, d'_3, t
  70. Vector(E'_2, H') → u_1
  71. Translate(B', u_1) → B''_2
  72. Translate(G, u_1) → G'_2
  73. Translate(A'_2, u_1) → U
  74. Translate(E'_2, u_1) → V
  75. Translate(C'_4, u_1) → W
  76. Translate(F'_2, u_1) → Z
  77. Translate(D'_2, u_1) → A_1
  78. Translate(H, u_1) → H'_2
  79. Polygon(B''_2, G'_2, U, V, W, Z, A_1, H'_2) → poly4''_2, b''_2, g'_2, u_2, v_1, w_1, z_1, a_4, h'_2
  80. Translate(B'_1, j_1) → B_1
  81. Translate(S, j_1) → S'
  82. Translate(A'_3, j_1) → C_1
  83. Translate(E'_3, j_1) → D_1
  84. Translate(C'_5, j_1) → E_1
  85. Translate(F'_3, j_1) → F_1
  86. Translate(D'_3, j_1) → G_1
  87. Translate(T, j_1) → T'
  88. Polygon(B_1, S', C_1, D_1, E_1, F_1, G_1, T') → poly5, b_3, s', c_5, d_4, e_3, f_3, g_2, t'
  89. Translate(B'_1, k_1) → H_1
  90. Translate(S, k_1) → S'_1
  91. Translate(A'_3, k_1) → I_1
  92. Translate(E'_3, k_1) → J_1
  93. Translate(C'_5, k_1) → K_1
  94. Translate(F'_3, k_1) → L_1
  95. Translate(D'_3, k_1) → M_1
  96. Translate(T, k_1) → T'_1
  97. Polygon(H_1, S'_1, I_1, J_1, K_1, L_1, M_1, T'_1) → poly6, h_2, s'_1, i_2, j_2, k_2, l_1, m_1, t'_1
  98. Vector(T, E) → p_1
  99. Translate(B'_1, p_1) → N_1
  100. Translate(S, p_1) → S'_2
  101. Translate(A'_3, p_1) → O_1
  102. Translate(E'_3, p_1) → P_1
  103. Translate(C'_5, p_1) → Q_1
  104. Translate(F'_3, p_1) → R_1
  105. Translate(D'_3, p_1) → S_1
  106. Translate(T, p_1) → T'_2
  107. Polygon(N_1, S'_2, O_1, P_1, Q_1, R_1, S_1, T'_2) → poly7, n_2, s'_2, o_1, p_2, q_1, r_1, s_2, t'_2
  108. Translate(B''_1, p_1) → T_1
  109. Translate(G'_1, p_1) → U_1
  110. Translate(N, p_1) → N'
  111. Translate(O, p_1) → O'
  112. Translate(P, p_1) → P'
  113. Translate(Q, p_1) → Q'
  114. Translate(R, p_1) → R'
  115. Translate(H'_1, p_1) → V_1
  116. Polygon(T_1, U_1, N', O', P', Q', R', V_1) → poly8, t_1, u_3, n', o', p', q', r', v_2
  117. Translate(B''_2, p_1) → W_1
  118. Translate(G'_2, p_1) → Z_1
  119. Translate(U, p_1) → U'
  120. Translate(V, p_1) → V'
  121. Translate(W, p_1) → W'
  122. Translate(Z, p_1) → Z'
  123. Translate(A_1, p_1) → A_2
  124. Translate(H'_2, p_1) → B_2
  125. Polygon(W_1, Z_1, U', V', W', Z', A_2, B_2) → poly9, w_2, z_2, u', v', w', z', a_5, b_4
  126. Translate(B, p_1) → B'_2
  127. Translate(F'_1, p_1) → C_2
  128. Translate(A, p_1) → A'_4
  129. Translate(E, p_1) → E'_4
  130. Translate(C, p_1) → C'_6
  131. Translate(F, p_1) → F'_4
  132. Translate(D, p_1) → D'_4
  133. Translate(E'_1, p_1) → D_2
  134. Polygon(B'_2, C_2, A'_4, E'_4, C'_6, F'_4, D'_4, D_2) → poly4'_2, b'_2, c_6, a'_4, e'_5, c'_6, f'_5, d'_4, d_5
  135. Translate(B', p_1) → B''_3
  136. Translate(G, p_1) → G'_3
  137. Translate(A'_2, p_1) → E_2
  138. Translate(E'_2, p_1) → F_2
  139. Translate(C'_4, p_1) → G_2
  140. Translate(F'_2, p_1) → H_2
  141. Translate(D'_2, p_1) → I_2
  142. Translate(H, p_1) → H'_3
  143. Polygon(B''_3, G'_3, E_2, F_2, G_2, H_2, I_2, H'_3) → poly4''_3, b''_3, g'_3, e_4, f_4, g_3, h_3, i_3, h'_3
  144. Translate(B'', p_1) → B'''
  145. Translate(G', p_1) → G''
  146. Translate(I, p_1) → I'
  147. Translate(J, p_1) → J'
  148. Translate(K, p_1) → K'
  149. Translate(L, p_1) → L'
  150. Translate(M, p_1) → M'
  151. Translate(H', p_1) → H''
  152. Polygon(B''', G'', I', J', K', L', M', H'') → poly4''', b''', g'', i', j', k', l', m', h''

AI Drawing Prompt Reference

Draw a geometric tessellation constructed using translation vectors and parallelograms. Start by creating a line segment and a parallel line, then connect their endpoints to form a parallelogram. Next, use a vector to translate the parallelogram and repeat this process to create multiple parallelograms. Finally, combine these shapes into a complex tessellation pattern, showcasing spatial transformations and geometric figure composition.
The prompt above was compiled from the original drawing commands and is for reference only.