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Rotational Symmetry Redux

Rotational Symmetry Redux
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2015-10-02 05:52
PolygonTransformationGeometric Construction
This example demonstrates rotational symmetry in geometric shapes. Key mathematical concepts include rotational symmetry and geometric transformations. Using GeoGebra commands such as Segment, OrthogonalLine, Point, Intersect, Polygon, Circle, Line, Rotate, Mirror, etc., one can construct polygons with rotational symmetry. Suitable for middle school and above students to learn about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Polygon(C, D, B, A) → poly1, c_1, d_1, b_1, a_1
  8. Segment(C, B) → e
  9. Segment(D, A) → f
  10. Polygon(F, G, 4) → poly2, f_1, g, h, i, H, I
  11. Segment(I, G) → j
  12. Segment(H, F) → k
  13. Segment(K, L) → l
  14. Circle(K, L) → p
  15. Point(p) → M
  16. Segment(K, M) → m
  17. Line(M, l) → n
  18. Line(L, m) → q
  19. Intersect(n, q) → N
  20. Segment(M, L) → r
  21. Segment(N, K) → s
  22. Polygon(M, N, L, K) → poly3, m_1, n_1, l_1, k_1
  23. Rotate(C, (-α), E) → C'
  24. Rotate(D, (-α), E) → D'
  25. Rotate(B, (-α), E) → B'
  26. Rotate(A, (-α), E) → A'
  27. Polygon(C', D', B', A') → poly1', c', d', b', a'
  28. Rotate(M, (-α), O) → M'
  29. Rotate(N, (-α), O) → N'
  30. Rotate(L, (-α), O) → L'
  31. Rotate(K, (-α), O) → K'
  32. Polygon(M', N', L', K') → poly3', m', n', l', k'
  33. Segment(P, Q) → t
  34. Segment(P, R) → e_1
  35. Line(Q, e_1) → g_1
  36. Line(R, t) → h_1
  37. Intersect(g_1, h_1) → S
  38. Polygon(P, R, S, Q) → poly4, p_1, r_1, s_1, q_1
  39. Segment(R, Q) → i_1
  40. Segment(S, P) → j_1
  41. Rotate(P, (-α), T) → P'
  42. Rotate(R, (-α), T) → R'
  43. Rotate(S, (-α), T) → S'
  44. Rotate(Q, (-α), T) → Q'
  45. Polygon(P', R', S', Q') → poly4', p', r', s', q'
  46. Segment(U, V) → t_1
  47. Segment(U, W) → a_2
  48. Line(W, t_1) → b_2
  49. Point(b_2) → Z
  50. Segment(Z, V) → c_2
  51. Polygon(U, V, Z, W) → poly5, u, v, z, w
  52. Segment(W, V) → d_2
  53. Segment(Z, U) → e_2
  54. Rotate(U, (-α), A_1) → U'
  55. Rotate(V, (-α), A_1) → V'
  56. Rotate(Z, (-α), A_1) → Z'
  57. Rotate(W, (-α), A_1) → W'
  58. Polygon(U', V', Z', W') → poly5', u', v', z', w'
  59. Line(B_1, C_1) → f_2
  60. Mirror(D_1, f_2) → E_1
  61. Polygon(D_1, B_1, E_1, C_1) → poly6, d_3, b_3, e_3, c_3
  62. Segment(D_1, E_1) → g_2
  63. Rotate(D_1, (-α), F_1) → G_1
  64. Rotate(B_1, (-α), F_1) → H_1
  65. Rotate(E_1, (-α), F_1) → I_1
  66. Rotate(C_1, (-α), F_1) → J_1
  67. Polygon(G_1, H_1, I_1, J_1) → poly6', g_3, h_2, i_2, j_2
  68. Rotate(poly2, (-α), J) → poly2'