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俄罗斯足球与数学构造

俄罗斯足球与数学构造
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2017-08-26 04:56
多边形向量立体几何矩阵几何作图
①本范例通过动态演示俄罗斯足球的几何构造，揭示其复杂的几何对称性与空间关系；②涉及的核心数学概念包括向量、矩阵变换、旋转、反射、多边形构造及正交中心；③作图要点提炼自构造摘要，运用了Point、Vector、Mirror、Polygon、Rotate、Segment、Sphere、OrthogonalPlane、Circle、Center、Ray、Intersect、Distance等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解空间几何、线性代数及变换理论的实际应用。

GeoGebra 命令及参数

  1. Point(zAxis) → H
  2. Vector(O, H) → u
  3. Mirror(A, yAxis) → A'
  4. Polygon(A, A', 8) → poly1, f, C, D, E, F, G, g, h, i, j, k, l, m, B
  5. Rotate(Translate[Lo, u], 22.5°, zAxis) → Lo'
  6. Point(Lo') → I
  7. Point(Lo') → J
  8. Point(Lo') → K
  9. Rotate(Lo', 90°, xAxis) → Lo''
  10. Rotate(Rotate[Lo', 90°, xAxis], 22.5°, yAxis) → liste1
  11. Rotate(Translate[Lo, u], 45°, zAxis) → poly1'
  12. Point(Lo') → L
  13. Point(Lo'') → M
  14. Segment(L, M) → n
  15. Rotate(Lo'', 90°, zAxis) → Lb
  16. Rotate(Lb, 90°, zAxis) → Lc
  17. Rotate(Lc, 90°, zAxis) → Ld
  18. Point(Lo') → N
  19. Sphere(O, N) → a
  20. Point(Lo') → P
  21. Point(Lb) → Q
  22. Segment(P, Q) → p
  23. Point(Lo'') → R
  24. Point(Lo'') → S
  25. OrthogonalPlane(O, xAxis) → d
  26. Point(Lb) → U
  27. Circle(N, S, U) → e
  28. Center(e) → V
  29. Sphere(O, N) → b
  30. Point(Lo'') → T
  31. Point(Lb) → W
  32. Segment(T, W) → t
  33. Ray(O, V) → c
  34. Intersect(c, b) → Z,
  35. Polygon(P, Q, U, Z, N) → poly2, p_1, q, u_1, z_1, n_1
  36. Segment(S, Z) → r
  37. Rotate(Z, 90°, zAxis) → Z'
  38. Rotate(Z', 90°, zAxis) → Z''
  39. Rotate(Z'', 90°, zAxis) → Z'''
  40. Point(Lo') → A_1
  41. Segment(A_1, Z''') → s
  42. Segment(R, Z''') → f_1
  43. Point(Ld) → B_1
  44. Segment(Z''', B_1) → g_1
  45. Point(Ld) → C_1
  46. Point(Lo') → D_1
  47. Segment(C_1, D_1) → h_1
  48. Point(Lo') → E_1
  49. Segment(E_1, Z'') → i_1
  50. Point(Ld) → F_1
  51. Segment(Z'', F_1) → j_1
  52. Point(Lc) → G_1
  53. Segment(Z'', G_1) → k_1
  54. Point(Lo') → H_1
  55. Segment(H_1, Z') → l_1
  56. Point(Lc) → I_1
  57. Segment(Z', I_1) → m_1
  58. Point(Lb) → J_1
  59. Segment(Z', J_1) → q_1
  60. Point(Lb) → K_1
  61. Point(Lc) → L_1
  62. Segment(K_1, L_1) → r_1
  63. Point(Lc) → M_1
  64. Point(Ld) → N_1
  65. Segment(M_1, N_1) → s_1
  66. Point(Ld) → O_1
  67. Point(Lo'') → P_1
  68. Segment(O_1, P_1) → t_1
  69. Point(Lc) → R_1
  70. Point(Lo') → S_1
  71. Segment(R_1, S_1) → a_1
  72. Point(Lo'') → Q_1
  73. Point(Lo'') → T_1
  74. Point(Lo'') → U_1
  75. Point(Lo'') → V_1
  76. Point(Lo'') → W_1
  77. Point(Lo'') → Z_1
  78. Point(Lo'') → A_2
  79. Point(Lo'') → B_2
  80. Rotate(Translate[poly1, u], 22.5°, zAxis) → poly4
  81. Rotate(poly4, 90°, xAxis) → poly4'
  82. Rotate(poly4', 90°, zAxis) → poly4''
  83. Rotate(poly4'', 90°, zAxis) → poly4'''
  84. Rotate(poly4', -90°, zAxis) → poly4''_1
  85. Mirror(poly4, O) → poly4'_1
  86. Distance(O, H) → distanceOH