Pattern Block Symmetry

Pattern Block Symmetry
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2017-09-22 02:58
In collections Symmetry Explorations
This example demonstrates how to create symmetrical shapes based on a given pattern. It involves core math concepts like symmetry, variance, congruence, circumcircle, cuboid, and coordinate geometry. Construction highlights include using GeoGebra commands such as Point, Segment, Polygon, Rotate, Angle, Circle, Intersect, and Midpoint. Suitable for middle school and above students exploring geometric symmetry.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → f
  3. Polygon(A, B, 6) → poly1, g, F, h, i, j, k, l, C, D, E
  4. Point(Circle[G, a]) → H
  5. Segment(G, H) → m
  6. Polygon(G, H, 3) → poly2, n, p, q, I
  7. Point(Circle[J, a]) → K
  8. Segment(J, K) → r
  9. Polygon(J, K, 3) → poly3, s, t, b, L
  10. Polygon(L, K, 3) → poly4, c, d, e, M
  11. Polygon(J, K, M, L) → poly5, j_1, k_1, m_1, l_1
  12. Point(Circle[S, a]) → T
  13. Segment(S, T) → a_1
  14. Polygon(S, T, 4) → poly10, b_1, c_1, d_1, e_1, U, V
  15. Point(Circle[W, a]) → Z
  16. Segment(W, Z) → f_2
  17. Rotate(Z, 30°, W) → Z'
  18. Angle(Z, W, Z') → α
  19. Circle(Z, W) → c_2
  20. Circle(Z', W) → d_2
  21. Intersect(c_2, d_2, 2) → A_1
  22. Polygon(W, Z, A_1, Z') → poly11, w, z_1, a_2, z'
  23. Point(Circle[A_2, a]) → B_1
  24. Segment(A_2, B_1) → f_3
  25. Polygon(A_2, B_1, 6) → poly1_1, g_2, F_1, h_2, i_2, j_2, k_2, l_2, C_1, D_1, E_1
  26. Point(Circle[W_1, a]) → Z_1
  27. Segment(W_1, Z_1) → f_4
  28. Rotate(Z_1, 30°, W_1) → Z'_1
  29. Angle(Z_1, W_1, Z'_1) → α_1
  30. Circle(Z_1, W_1) → c_3
  31. Circle(Z'_1, W_1) → d_3
  32. Intersect(c_3, d_3, 2) → A_3
  33. Point(Circle[W_2, a]) → Z_2
  34. Segment(W_2, Z_2) → f_5
  35. Rotate(Z_2, 30°, W_2) → Z'_2
  36. Angle(Z_2, W_2, Z'_2) → α_2
  37. Circle(Z_2, W_2) → c_4
  38. Circle(Z'_2, W_2) → d_4
  39. Intersect(c_4, d_4, 2) → A_4
  40. Polygon(W_2, Z_2, A_4, Z'_2) → poly11_1, w_1, z_2, a_3, z'_1
  41. Point(Circle[G_1, (2 * a)]) → H_1
  42. Segment(G_1, H_1) → m_2
  43. Polygon(G_1, H_1, 3) → poly12, s_2, t_2, b_2, I_1
  44. Midpoint(G_1, I_1) → J_1
  45. Midpoint(H_1, I_1) → K_1
  46. Polygon(G_1, H_1, K_1, J_1) → poly13, g_3, h_3, k_3, j_3
  47. Point(Circle[G_2, (2 * a)]) → H_2
  48. Segment(G_2, H_2) → m_3
  49. Polygon(G_2, H_2, 3) → poly12_1, s_3, t_3, b_3, I_2
  50. Midpoint(G_2, I_2) → J_2
  51. Midpoint(H_2, I_2) → K_2
  52. Polygon(G_2, H_2, K_2, J_2) → poly13_1, g_4, h_4, k_4, j_4
  53. Point(Circle[G_3, a]) → H_3
  54. Segment(G_3, H_3) → m_4
  55. Polygon(G_3, H_3, 3) → poly2_1, n_1, p_1, q_1, I_3
  56. Point(Circle[J_3, a]) → K_3
  57. Segment(J_3, K_3) → r_1
  58. Polygon(J_3, K_3, 3) → poly3_1, s_1, t_1, b_4, L_1
  59. Polygon(L_1, K_3, 3) → poly4_1, c_5, d_5, e_2, M_1
  60. Polygon(J_3, K_3, M_1, L_1) → poly5_1, j_5, k_5, m_5, l_3
  61. Point(Circle[W_3, a]) → Z_3
  62. Segment(W_3, Z_3) → f_1
  63. Rotate(Z_3, 30°, W_3) → Z'_3
  64. Angle(Z_3, W_3, Z'_3) → α_3
  65. Circle(Z_3, W_3) → c_6
  66. Circle(Z'_3, W_3) → d_6
  67. Intersect(c_6, d_6, 2) → A_5
  68. Polygon(W_3, Z_3, A_5, Z'_3) → poly11_2, w_2, z_3, a_4, z'_2
  69. Point(Circle[G_4, (2 * a)]) → H_4
  70. Segment(G_4, H_4) → m_6
  71. Polygon(G_4, H_4, 3) → poly12_2, s_4, t_4, b_5, I_4
  72. Midpoint(G_4, I_4) → J_4
  73. Midpoint(H_4, I_4) → K_4
  74. Polygon(G_4, H_4, K_4, J_4) → poly13_2, g_1, h_1, k_6, j_6
  75. Point(Circle[J_5, a]) → K_5
  76. Segment(J_5, K_5) → r_2
  77. Polygon(J_5, K_5, 3) → poly3_2, s_5, t_5, b_6, L_2
  78. Polygon(L_2, K_5, 3) → poly4_2, c_7, d_7, e_3, M_2
  79. Polygon(J_5, K_5, M_2, L_2) → poly5_2, j_7, k_7, m_7, l_4

AI Drawing Prompt Reference

Create a symmetric pattern composed of multiple geometric shapes. Start with a regular hexagon based on a point on a circle. Then add a regular triangle adjacent to it, followed by two more triangles sharing sides to form a rhombus-like arrangement. Construct a square, and a rhombus formed by two intersecting circles and a rotated point. Repeat these elements: another hexagon, two rhombi, and a larger triangle. Inside the larger triangle, connect midpoints to form a quadrilateral. Arrange all shapes symmetrically around a central axis for a balanced, mirrored composition.
The prompt above was compiled from the original drawing commands and is for reference only.