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梅赛德斯标志的数学构造

梅赛德斯标志的数学构造
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2019-04-30 00:26
圆多边形向量
①本范例演示了如何使用二维向量和几何变换构造梅赛德斯汽车标志；②涉及的核心数学概念包括向量、圆、椭圆、多边形、旋转、镜像、中点、角平分线等；③作图要点：使用了Circle（圆）、Vector（向量）、Line（线）、Rotate（旋转）、LineBisector（角平分线）、Polygon（多边形）、Mirror（镜像）、Segment（线段）、Midpoint（中点）、AngularBisector（角平分线）、Intersect（交点）、CircleArc（圆弧）、CircleSector（圆扇形）等GeoGebra命令；④适合高中数学教学，用于展示几何变换和图形构造的实践应用。

GeoGebra 命令及参数

  1. Circle(O, A) → c
  2. Vector(O, A) → u
  3. Circle(O, B) → d
  4. Line(A, O) → f
  5. Rotate(B, 120°, O) → B'
  6. Rotate(B, (-(120°)), O) → B'_1
  7. Rotate(B, 1°, O) → B'_2
  8. Rotate(B, -1°, O) → B'_3
  9. Rotate(B', 1°, O) → B''
  10. Rotate(B', -1°, O) → B''_1
  11. Rotate(B'_1, 1°, O) → C
  12. Rotate(B'_1, -1°, O) → D
  13. LineBisector(B, B') → g
  14. LineBisector(B, B'_1) → h
  15. Rotate(E, 120°, O) → E'
  16. Rotate(E, (-(120°)), O) → E'_1
  17. Polygon(E'_1, O, B, B'_2) → c1, e'_1, o, b, b'_2
  18. Mirror(E'_1, g) → F
  19. Mirror(O, g) → O'
  20. Mirror(B, g) → B'_4
  21. Mirror(B'_2, g) → G
  22. Polygon(F, O', B'_4, G) → c1', f_1, o', b'_4, g_1
  23. Mirror(F, f) → F'
  24. Mirror(O', f) → O''
  25. Mirror(B'_4, f) → H
  26. Mirror(G, f) → G'
  27. Polygon(F', O'', H, G') → c1'', f', o'', h_1, g'
  28. Polygon(B'_3, B, O, E') → c2, b'_3, b_1, o_1, e'
  29. Mirror(B'', f) → B'''
  30. Mirror(B', f) → B''_2
  31. Mirror(O, f) → O'_1
  32. Mirror(E, f) → E'_2
  33. Segment(O, E) → i
  34. Segment(O, F') → j
  35. Segment(O, F) → k
  36. Circle(O, I) → p
  37. Midpoint(F, O) → J
  38. Midpoint(F, J) → K
  39. Midpoint(J, O) → L
  40. Polygon(I, K, L) → t1, l, i_1, k_1
  41. Mirror(I, g) → I'
  42. Mirror(K, g) → K'
  43. Mirror(L, g) → L'
  44. Polygon(I', K', L') → t1', l', i', k'
  45. Mirror(I', f) → I''
  46. Mirror(K', f) → K''
  47. Mirror(L', f) → L''
  48. Polygon(I'', K'', L'') → t1'', l'', i'', k''
  49. Midpoint(O, F') → M
  50. Polygon(I, O, M) → t2, m, i_2, o_3
  51. AngularBisector(F', O, B'_1) → n
  52. Intersect(d, n) → N, P
  53. Mirror(O, o_3) → O'_2
  54. Mirror(M, o_3) → M'
  55. Segment(O'_2, M') → j_1
  56. Intersect(p, n) → Q, R
  57. CircleArc(O, B, B') → q
  58. CircleArc(O, I, I') → r
  59. CircleArc(O, I, B') → s
  60. Rotate(B, 4°, O) → B'_5
  61. CircleArc(O, P, B'_5) → t
  62. CircleArc(O, R, I) → e_1
  63. CircleArc(O, R, I) → p_1
  64. CircleArc(O, P, B') → q_1
  65. Intersect(c, n) → G_1, G_2
  66. Intersect(c, h) → U, V
  67. Intersect(c, f) → W, Z
  68. AngularBisector(U, O, Z) → l_1
  69. Intersect(c, l_1) → A_1, B_1
  70. AngularBisector(U, O, B_1) → m_1
  71. Intersect(c, m_1) → C_1, D_1
  72. Intersect(c, g) → E_1, F_1
  73. CircleArc(O, U, B'_1) → c_1
  74. CircleArc(O, B', B'_1) → d_1
  75. CircleArc(O, I', I'') → r_1
  76. CircleArc(O, U, F_1) → s_1
  77. CircleArc(O, I', I'') → t_1
  78. CircleArc(O, G_1, B') → c_2
  79. Polygon(G_1, N, B', U) → c4, n_1, n_2, a_1, u_1
  80. CircleArc(O, F_1, G_2) → d_2
  81. Polygon(G_2, P, B'_1, F_1) → c5, g_2, p_2, b'_1, f_2
  82. CircleArc(O, B'_1, P) → e_2
  83. CircleArc(O, I'', R) → k_2
  84. CircleArc(O, I'', R) → q_2
  85. CircleArc(O, G_2, V) → s_2
  86. Intersect(d, t, 1) → T
  87. Intersect(d, h) → I_1, J_1
  88. Polygon(V, J_1, T, G_2) → c7, v, l_2, t_2, m_2
  89. CircleArc(O, V, C_1) → c_3
  90. Intersect(d, m_1) → K_1, L_1
  91. Polygon(C_1, K_1, J_1, V) → c8, a_2, b_2, f_3, v_1
  92. Intersect(d, l_1) → S, H_1
  93. Polygon(A_1, S, K_1, C_1) → c9, g_3, s_3, h_3, i_3
  94. CircleArc(O, A_1, A) → d_3
  95. Polygon(A, A_1, S, B) → c10, a_3, j_3, s_4, b_3
  96. Rotate(P, 8°, O) → P'
  97. Rotate(R, 8°, O) → R'
  98. Rotate(I'', (-(4°)), O'') → I'''
  99. Line(O'', B'') → e
  100. Intersect(c, e) → M_1, N_1
  101. Rotate(N_1, -1°, O) → O_1
  102. Polygon(O_1, N_1, E, O) → c3, j_2, k_3, e_3, o_2
  103. Rotate(B'', 2°, O) → B'''_1
  104. CircleSector(O, B''_1, B'''_1) → q_3
  105. Mirror(q_3, f) → t_3
  106. Mirror(O_1, f) → P_1
  107. Mirror(N_1, f) → Q_1
  108. Mirror(E, f) → E'_3
  109. Mirror(O, f) → O'_3
  110. Polygon(P_1, Q_1, E'_3, O'_3) → c3', l_3, m_3, e'_3, o'_3
  111. Polygon(R, G_2, B'_1, I'') → c6, r_2, h_2, n_3, p_3
  112. CircleArc(O, I'', R) → c_4
  113. Segment(I, R) → r_3
  114. Vector(O, F') → w
  115. Intersect(c_4, n_3, 1) → S_1
  116. Polygon(R_1, O, S_1) → t3, f_4, g_4, o_4
  117. Polygon(R, P, R') → t4, r', r_4, p_4
  118. CircleArc(O, S_1, R) → d_4
  119. Intersect(r', r_4) → T_1
  120. CircleArc(O, C, T_1) → e_4