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Introduction to Rotational Symmetry

Introduction to Rotational Symmetry
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2014-06-12 20:14
PolygonTransformationGeometric Construction
This example demonstrates the concept of rotational symmetry in polygons. Key math concepts include symmetry, axes of symmetry, and center of rotation. It is constructed using GeoGebra commands like Polygon, Segment, Rotate, Midpoint, Line, Intersect, and OrthogonalLine. Suitable for middle school students and above learning geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, a, b, c, d, e, C, D, E
  2. Polygon(F, N, G, M, H, O, J, L) → poly2, f, n, g, m, h, o, j, l
  3. Segment(I, K) → i
  4. Segment(K, P) → k
  5. Segment(P, Q) → p
  6. Rotate(K, 240*°, R) → K'
  7. Rotate(P, 240*°, R) → P'
  8. Segment(K', P') → k'
  9. Rotate(K', 240*°, R) → K''
  10. Rotate(P', 240*°, R) → P''
  11. Segment(K'', P'') → k''
  12. Rotate(P, 240*°, R) → P'_1
  13. Rotate(Q, 240*°, R) → Q'
  14. Segment(P'_1, Q') → p'
  15. Rotate(I, 120*°, R) → I'
  16. Rotate(K, 120*°, R) → K'_1
  17. Segment(I', K'_1) → i'
  18. Rotate(I, 240*°, R) → I'_1
  19. Rotate(K, 240*°, R) → K'_2
  20. Segment(I'_1, K'_2) → i'_1
  21. Rotate(P, 120*°, R) → P'_2
  22. Rotate(Q, 120*°, R) → Q'_1
  23. Segment(P'_2, Q'_1) → p'_1
  24. Segment(I, Q'_1) → q
  25. Segment(Q, I'_1) → r
  26. Segment(Q', I') → s
  27. Polygon(K, P, Q'_1, I, Q, I'_1, K', P', Q', I', K'', P'') → poly3, k_1, p'', q'_1, i_1, p_1, q_1, i'_2, k'_1, p'_2, q', i'_3, k''_1
  28. Polygon(S, T, U, V) → poly4, s_1, t, u, v
  29. Midpoint(N, O) → W
  30. Midpoint(S, T) → Z
  31. Midpoint(S, V) → A_1
  32. Line(A_1, s_1) → a_1
  33. Line(Z, t) → b_1
  34. Intersect(a_1, b_1) → B_1
  35. OrthogonalLine(D, a) → c_1
  36. OrthogonalLine(C, e) → d_1
  37. Intersect(c_1, d_1) → C_1
  38. Rotate(poly1, w°, C_1) → poly1'
  39. Rotate(F, w°, W) → F'
  40. Rotate(N, w°, W) → N'
  41. Rotate(G, w°, W) → G'
  42. Rotate(M, w°, W) → M'
  43. Rotate(H, w°, W) → H'
  44. Rotate(O, w°, W) → O'
  45. Rotate(J, w°, W) → J'
  46. Rotate(L, w°, W) → L'
  47. Polygon(F', N', G', M', H', O', J', L') → poly2', f', n', g', m', h', o', j', l'
  48. Rotate(K, w°, R) → K'_3
  49. Rotate(P, w°, R) → P'_3
  50. Rotate(Q, w°, R) → Q'_2
  51. Rotate(I'_1, w°, R) → D_1
  52. Rotate(K', w°, R) → K''_1
  53. Rotate(P', w°, R) → P''_1
  54. Rotate(Q', w°, R) → Q''
  55. Rotate(I', w°, R) → I''
  56. Rotate(K'', w°, R) → K'''
  57. Rotate(P'', w°, R) → P'''
  58. Rotate(Q'_1, w°, R) → E_1
  59. Rotate(I, w°, R) → I'_2
  60. Polygon(K'_3, P'_3, E_1, I'_2, Q'_2, D_1, K''_1, P''_1, Q'', I'', K''', P''') → poly3', k'_3, p''', e_1, i'_4, p'_3, q'_2, d_2, k''_2, p''_1, q'', i'', k'''
  61. Rotate(S, w°, B_1) → S'
  62. Rotate(T, w°, B_1) → T'
  63. Rotate(U, w°, B_1) → U'
  64. Rotate(V, w°, B_1) → V'
  65. Polygon(S', T', U', V') → poly4', s', t', u', v'
  66. Polygon(F_1, G_1, H_1) → poly5, h_1, f_1, g_1
  67. OrthogonalLine(G_1, g_1) → j_1
  68. Intersect(j_1, g_1) → I_1
  69. Midpoint(I_1, G_1) → J_1
  70. Rotate(F_1, w°, J_1) → K_1
  71. Rotate(G_1, w°, J_1) → L_1
  72. Rotate(H_1, w°, J_1) → M_1
  73. Polygon(K_1, L_1, M_1) → poly5', m_1, k_2, l_1

AI Drawing Prompt Reference

Draw a pentagon and rotate it around its center three times, each time by 120 degrees, to create a symmetric pattern. Connect the rotated vertices to form a new polygon. Then, draw two line segments and find their intersection point. Rotate the pentagon by a certain angle around this intersection point, and also rotate the other polygon by the same angle to demonstrate rotational symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.