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旋转对称 by MiGunning03

旋转对称 by MiGunning03
几何画板及绘图内容加载中，请稍等……
2018-01-16 23:25
多边形变换几何作图
这个范例演示了旋转对称图形的构造。核心数学概念包括旋转对称性和几何作图。通过使用GeoGebra命令如Rotate、Angle、Polygon等，可以构造出具有旋转对称性的多边形。适合初中及以上学生学习旋转对称性及其应用。

GeoGebra 命令及参数

  1. Line(Q_1, P_1) → f_3
  2. Polygon(P_1, Q_1, 5) → poly7, l_2, m_2, n_2, p_2, q_2, R_1, S_1, T_1
  3. Line(R_1, Q_1) → h_3
  4. Intersect(h_3, f_3) → D_2
  5. Line(S_1, T_1) → t_2
  6. Intersect(t_2, f_3) → V_1
  7. Line(R_1, S_1) → s_2
  8. Line(P_1, T_1) → r_2
  9. Intersect(s_2, r_2) → U_1
  10. Segment(U_1, D_2) → k_3
  11. Mirror(V_1, k_3) → U_2
  12. Segment(A, B) → a
  13. OrthogonalLine(A, a) → b
  14. OrthogonalLine(B, a) → c
  15. Point(b) → C
  16. OrthogonalLine(C, b) → d
  17. Intersect(c, d) → D
  18. Polygon(C, D, B, A) → poly1, c_1, d_1, b_1, a_1
  19. Segment(C, B) → e
  20. Segment(D, A) → f
  21. Intersect(e, f) → E
  22. Polygon(F, G, 4) → poly2, f_1, g, h, i, H, I
  23. Segment(I, G) → j
  24. Segment(H, F) → k
  25. Intersect(j, k) → J
  26. Segment(K, L) → l
  27. Circle(K, L) → p
  28. Point(p) → M
  29. Segment(K, M) → m
  30. Line(M, l) → n
  31. Line(L, m) → q
  32. Intersect(n, q) → N
  33. Segment(M, L) → r
  34. Segment(N, K) → s
  35. Intersect(r, s) → O
  36. Polygon(M, N, L, K) → poly3, m_1, n_1, l_1, k_1
  37. Rotate(C, (-α), E) → C'
  38. Rotate(D, (-α), E) → D'
  39. Rotate(B, (-α), E) → B'
  40. Rotate(A, (-α), E) → A'
  41. Polygon(C', D', B', A') → Rectangle, c', d', b', a'
  42. Rotate(M, (-α), O) → M'
  43. Rotate(N, (-α), O) → N'
  44. Rotate(L, (-α), O) → L'
  45. Rotate(K, (-α), O) → K'
  46. Polygon(M', N', L', K') → Rhombus, m', n', l', k'
  47. Segment(P, Q) → t
  48. Segment(P, R) → e_1
  49. Line(Q, e_1) → g_1
  50. Line(R, t) → h_1
  51. Intersect(g_1, h_1) → S
  52. Polygon(P, R, S, Q) → poly4, p_1, r_1, s_1, q_1
  53. Segment(R, Q) → i_1
  54. Segment(S, P) → j_1
  55. Intersect(i_1, j_1) → T
  56. Rotate(P, (-α), T) → P'
  57. Rotate(R, (-α), T) → R'
  58. Rotate(S, (-α), T) → S'
  59. Rotate(Q, (-α), T) → Q'
  60. Polygon(P', R', S', Q') → Parallelogram, p', r', s', q'
  61. Segment(U, V) → t_1
  62. Segment(U, W) → a_2
  63. Line(W, t_1) → b_2
  64. Point(b_2) → Z
  65. Segment(Z, V) → c_2
  66. Polygon(U, V, Z, W) → poly5, u, v, z, w
  67. Segment(W, V) → d_2
  68. Segment(Z, U) → e_2
  69. Intersect(d_2, e_2) → A_1
  70. Rotate(U, (-α), A_1) → U'
  71. Rotate(V, (-α), A_1) → V'
  72. Rotate(Z, (-α), A_1) → Z'
  73. Rotate(W, (-α), A_1) → W'
  74. Polygon(U', V', Z', W') → Trapezoid, u', v', z', w'
  75. Line(B_1, C_1) → f_2
  76. Mirror(D_1, f_2) → E_1
  77. Polygon(D_1, B_1, E_1, C_1) → poly6, d_3, b_3, e_3, c_3
  78. Segment(D_1, E_1) → g_2
  79. Intersect(f_2, g_2) → F_1
  80. Rotate(D_1, (-α), F_1) → G_1
  81. Rotate(B_1, (-α), F_1) → H_1
  82. Rotate(E_1, (-α), F_1) → I_1
  83. Rotate(C_1, (-α), F_1) → J_1
  84. Polygon(G_1, H_1, I_1, J_1) → Kite, g_3, h_2, i_2, j_2
  85. Rotate(poly2, (-α), J) → Square
  86. Line(K_1, L_1) → k_2
  87. Circle(M_1, N_1) → Circle
  88. Rotate(N_1, α, M_1) → O_1
  89. Angle(N_1, M_1, O_1) → β
  90. Intersect(r_2, h_3) → W_1
  91. Intersect(f_3, s_2) → Z_1
  92. Intersect(h_3, t_2) → A_2
  93. Intersect(r_2, t_2) → B_2
  94. Intersect(f_3, r_2) → C_2
  95. Intersect(s_2, h_3) → E_2
  96. Intersect(s_2, t_2) → F_2
  97. Polygon(U_1, B_2, V_1, C_2, W_1, D_2, Z_1, E_2, G_2, F_2) → poly8, u_1, f_4, b_4, v_1, c_4, w_1, d_4, z_1, e_4, g_4
  98. Line(H_2, I_2) → i_3
  99. Mirror(J_2, i_3) → O_2
  100. Mirror(K_2, i_3) → P_2
  101. Mirror(L_2, i_3) → Q_2
  102. Mirror(M_2, i_3) → R_2
  103. Mirror(N_2, i_3) → S_2
  104. Polygon(J_2, O_2, P_2, Q_2, R_2, S_2, N_2, M_2, L_2, T_2) → poly9, j_3, t_3, o_2, p_3, q_3, r_3, s_3, n_3, m_3, l_3