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Kaleidoscope Pattern Transformation

Kaleidoscope Pattern Transformation
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2016-04-16 00:16
TransformationGeometric ConstructionSlider Animation
This example demonstrates geometric transformations such as reflection, rotation, and translation by dragging red points to change shapes and patterns. Commands used include Line, Circle, Intersect, Segment, Dilate, Polygon, Mirror, and Rotate. Suitable for middle school and above students to learn about geometric transformations and pattern design.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Circle(A, B) → c
  3. Circle(B, A) → d
  4. Intersect(c, d, 1) → C
  5. Circle(C, A) → e
  6. Intersect(c, d, 2) → D
  7. Circle(D, A) → f
  8. Intersect(c, e, 1) → E
  9. Intersect(c, a, 2) → F
  10. Intersect(c, f, 2) → G
  11. Line(E, A) → b
  12. Line(C, A) → g
  13. Segment(H, I) → h
  14. Segment(J, K) → i
  15. Segment(L, M) → j
  16. Segment(N, O) → k
  17. Segment(P, Q) → l
  18. Segment(R, S) → m
  19. Segment(T, U) → n
  20. Segment(V, W) → p
  21. Dilate(I, 0.5 + (0.5 * cos(o)), H) → I'
  22. Dilate(L, 0.5 + (0.5 * cos(o)), M) → L'
  23. Dilate(Q, 0.5 + (0.5 * cos(o)), P) → Q'
  24. Dilate(T, 0.5 + (0.5 * cos(o)), U) → T'
  25. Dilate(J, 0.5 + (0.5 * sin(o)), K) → J'
  26. Dilate(O, 0.5 + (0.5 * sin(o)), N) → O'
  27. Dilate(R, 0.5 + (0.5 * sin(o)), S) → R'
  28. Dilate(W, 0.5 + (0.5 * sin(o)), V) → W'
  29. Polygon(I', J', L', O', Q', R', T', W') → poly1, i', j', l', o', q', r', t', w'
  30. Mirror(I', g) → I''
  31. Mirror(J', g) → J''
  32. Mirror(L', g) → L''
  33. Mirror(O', g) → O''
  34. Mirror(Q', g) → Q''
  35. Mirror(R', g) → R''
  36. Mirror(T', g) → T''
  37. Mirror(W', g) → W''
  38. Polygon(I'', J'', L'', O'', Q'', R'', T'', W'') → poly1', i'', j'', l'', o'', q'', r'', t'', w''
  39. Mirror(I'', b) → I'''
  40. Mirror(J'', b) → J'''
  41. Mirror(L'', b) → L'''
  42. Mirror(O'', b) → O'''
  43. Mirror(Q'', b) → Q'''
  44. Mirror(R'', b) → R'''
  45. Mirror(T'', b) → T'''
  46. Mirror(W'', b) → W'''
  47. Polygon(I''', J''', L''', O''', Q''', R''', T''', W''') → poly1'', i''', j''', l''', o''', q''', r''', t''', w'''
  48. Mirror(I''', a) → Z
  49. Mirror(J''', a) → A_1
  50. Mirror(L''', a) → B_1
  51. Mirror(O''', a) → C_1
  52. Mirror(Q''', a) → D_1
  53. Mirror(R''', a) → E_1
  54. Mirror(T''', a) → F_1
  55. Mirror(W''', a) → G_1
  56. Polygon(Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1) → poly1''', z_1, a_1, b_1, c_1, d_1, e_1, f_1, g_1
  57. Mirror(Z, g) → Z'
  58. Mirror(A_1, g) → H_1
  59. Mirror(B_1, g) → I_1
  60. Mirror(C_1, g) → J_1
  61. Mirror(D_1, g) → K_1
  62. Mirror(E_1, g) → L_1
  63. Mirror(F_1, g) → M_1
  64. Mirror(G_1, g) → N_1
  65. Polygon(Z', H_1, I_1, J_1, K_1, L_1, M_1, N_1) → poly2, z', h_1, i_1, j_1, k_1, l_1, m_1, n_1
  66. Mirror(Z', b) → Z''
  67. Mirror(H_1, b) → O_1
  68. Mirror(I_1, b) → P_1
  69. Mirror(J_1, b) → Q_1
  70. Mirror(K_1, b) → R_1
  71. Mirror(L_1, b) → S_1
  72. Mirror(M_1, b) → T_1
  73. Mirror(N_1, b) → U_1
  74. Polygon(Z'', O_1, P_1, Q_1, R_1, S_1, T_1, U_1) → poly2', z'', o_1, p_1, q_1, r_1, s_1, t_1, u_1
  75. Rotate(I', 60°, A) → I''_1
  76. Rotate(J', 60°, A) → J''_1
  77. Rotate(L', 60°, A) → L''_1
  78. Rotate(O', 60°, A) → O''_1
  79. Rotate(Q', 60°, A) → Q''_1
  80. Rotate(R', 60°, A) → R''_1
  81. Rotate(T', 60°, A) → T''_1
  82. Rotate(W', 60°, A) → W''_1
  83. Polygon(I''_1, J''_1, L''_1, O''_1, Q''_1, R''_1, T''_1, W''_1) → poly1'_1, i''_1, j''_1, l''_1, o''_1, q''_1, r''_1, t''_1, w''_1
  84. Mirror(I''_1, b) → V_1
  85. Mirror(J''_1, b) → W_1
  86. Mirror(L''_1, b) → Z_1
  87. Mirror(O''_1, b) → A_2
  88. Mirror(Q''_1, b) → B_2
  89. Mirror(R''_1, b) → C_2
  90. Mirror(T''_1, b) → D_2
  91. Mirror(W''_1, b) → E_2
  92. Polygon(V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2) → poly3, v_1, w_1, z_2, a_2, b_2, c_2, d_2, e_2
  93. Mirror(V_1, a) → F_2
  94. Mirror(W_1, a) → G_2
  95. Mirror(Z_1, a) → H_2
  96. Mirror(A_2, a) → I_2
  97. Mirror(B_2, a) → J_2
  98. Mirror(C_2, a) → K_2
  99. Mirror(D_2, a) → L_2
  100. Mirror(E_2, a) → M_2
  101. Polygon(F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2) → poly3', f_2, g_2, h_2, i_2, j_2, k_2, l_2, m_2
  102. Mirror(F_2, g) → N_2
  103. Mirror(G_2, g) → O_2
  104. Mirror(H_2, g) → P_2
  105. Mirror(I_2, g) → Q_2
  106. Mirror(J_2, g) → R_2
  107. Mirror(K_2, g) → S_2
  108. Mirror(L_2, g) → T_2
  109. Mirror(M_2, g) → U_2
  110. Polygon(N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2) → poly3'', n_2, o_2, p_2, q_2, r_2, s_2, t_2, u_2
  111. Mirror(N_2, b) → V_2
  112. Mirror(O_2, b) → W_2
  113. Mirror(P_2, b) → Z_2
  114. Mirror(Q_2, b) → A_3
  115. Mirror(R_2, b) → B_3
  116. Mirror(S_2, b) → C_3
  117. Mirror(T_2, b) → D_3
  118. Mirror(U_2, b) → E_3
  119. Polygon(V_2, W_2, Z_2, A_3, B_3, C_3, D_3, E_3) → poly3''', v_2, w_2, z_3, a_3, b_3, c_3, d_3, e_3
  120. Mirror(V_2, a) → F_3
  121. Mirror(W_2, a) → G_3
  122. Mirror(Z_2, a) → H_3
  123. Mirror(A_3, a) → I_3
  124. Mirror(B_3, a) → J_3
  125. Mirror(C_3, a) → K_3
  126. Mirror(D_3, a) → L_3
  127. Mirror(E_3, a) → M_3
  128. Polygon(F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3) → poly4, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_3

AI Drawing Prompt Reference

Create a symmetrical hexagonal pattern by first drawing two intersecting lines a and b, then drawing two circles c and d with their intersection as the center, followed by circles e and f through points C and D, and circles g and h through points E and F. Draw segments i to p, then dilate these segments around the intersection points using cosine and sine values to create polygon poly1. Mirror poly1 across lines g and b, and finally mirror the result across line a to obtain the final hexagonal pattern Z.
The prompt above was compiled from the original drawing commands and is for reference only.