初学者梅特罗顿之立方体

初学者梅特罗顿之立方体
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2014-09-15 04:49
①本范例演示如何创建梅特罗顿之立方体,即由13个圆及其中心连线构成的几何图形;②涉及的核心数学概念包括圆、中心、线段、几何作图、对称性;③作图要点——使用了GeoGebra的Intersect(交点)、Circle(圆)、Point(点)、Segment(线段)、Ellipse(椭圆)等命令和对象;④适合初学者学习几何作图、空间想象及对称性概念,可作为基础几何教学或兴趣探索工具。

GeoGebra 命令及参数

  1. Intersect(a, b) → A
  2. Circle(A, B) → c
  3. Point(yAxis) → G
  4. Intersect(c, yAxis, 2) → H
  5. Circle(G, H) → f
  6. Point(yAxis) → I
  7. Intersect(f, yAxis, 2) → J
  8. Circle(I, J) → g
  9. Intersect(c, b, 2) → D
  10. Circle(D, A) → d
  11. Intersect(d, b, 2) → F
  12. Circle(F, D) → e
  13. Intersect(c, a, 2) → K
  14. Circle(K, A) → h
  15. Intersect(h, a, 2) → L
  16. Circle(L, K) → k
  17. Intersect(k, a, 2) → M
  18. Circle(M, L) → p
  19. Intersect(p, a, 2) → N
  20. Circle(N, M) → q
  21. Intersect(c, b, 1) → O
  22. Circle(O, A) → r
  23. Intersect(r, b, 2) → P
  24. Circle(P, O) → s
  25. Intersect(s, b, 2) → Q
  26. Circle(Q, P) → t
  27. Intersect(t, b, 2) → R
  28. Circle(R, Q) → c_1
  29. Intersect(c_1, b, 2) → S
  30. Circle(S, R) → d_1
  31. Circle(D, A) → e_1
  32. Intersect(e_1, b, 2) → T
  33. Circle(T, D) → f_1
  34. Intersect(f_1, b, 2) → U
  35. Circle(U, T) → g_1
  36. Intersect(g_1, b, 2) → V
  37. Circle(V, U) → h_1
  38. Intersect(c, r, 1) → W
  39. Circle(W, A) → k_1
  40. Intersect(k_1, a, 2) → Z
  41. Circle(Z, W) → p_1
  42. Intersect(p_1, a, 1) → A_1
  43. Circle(A_1, Z) → q_1
  44. Intersect(q_1, a, 2) → B_1
  45. Circle(B_1, A_1) → r_1
  46. Circle(R, Q) → s_1
  47. Point(yAxis) → C
  48. Intersect(c, yAxis, 1) → E
  49. Circle(C, E) → t_1
  50. Point(yAxis) → C_1
  51. Intersect(t_1, yAxis, 2) → D_1
  52. Circle(C_1, D_1) → c_2
  53. Segment(P, Z) → i
  54. Segment(P, G) → j
  55. Segment(G, L) → l
  56. Segment(L, T) → m
  57. Segment(Z, C) → n
  58. Segment(C, T) → a_1
  59. Segment(B_1, C_1) → b_1
  60. Segment(B_1, R) → i_1
  61. Segment(R, I) → j_1
  62. Segment(I, N) → l_1
  63. Segment(N, V) → m_1
  64. Segment(C_1, V) → n_1
  65. Segment(I, V) → a_2
  66. Segment(I, B_1) → b_2
  67. Segment(B_1, V) → d_2
  68. Segment(N, R) → e_2
  69. Segment(R, C_1) → f_2
  70. Segment(C_1, N) → g_2
  71. Segment(P, A) → h_2
  72. Segment(A, L) → i_2
  73. Segment(A, C) → j_2
  74. Segment(I, G) → k_2
  75. Segment(N, L) → l_2
  76. Segment(T, V) → m_2
  77. Segment(C, C_1) → n_2
  78. Segment(B_1, Z) → p_2
  79. Segment(R, P) → q_2
  80. Segment(A, Z) → r_2
  81. Segment(A, T) → s_2
  82. Segment(G, A) → t_2
  83. Segment(L, C) → a_3
  84. Segment(L, P) → b_3
  85. Segment(P, C) → c_3
  86. Segment(G, Z) → d_3
  87. Segment(G, T) → e_3
  88. Segment(Z, T) → f_3
  89. Intersect(j_1, l_1) → E_1
  90. Intersect(b_1, n_1) → F_1
  91. Intersect(m_1, a_2) → G_1
  92. Ellipse(E_1, F_1, G_1) → g_3
  93. Intersect(g_3, i_1, 1) → H_1
  94. Ellipse(H_1, G_1, F_1) → h_3
  95. Intersect(g_3, h_3, 1) → I_1
  96. Intersect(g_3, h_3, 4) → J_1
  97. Ellipse(I_1, J_1, F_1) → k_3
  98. Intersect(h_3, k_3, 3) → K_1
  99. Intersect(h_3, k_3, 2) → L_1
  100. Segment(K_1, L_1) → i_3
  101. Intersect(g_3, h_3, 2) → M_1
  102. Intersect(g_3, h_3, 3) → N_1
  103. Segment(M_1, N_1) → j_3
  104. Intersect(g_3, k_3, 1) → O_1
  105. Intersect(g_3, k_3, 4) → P_1
  106. Segment(O_1, P_1) → l_3

AI 绘图提示语参考

画一个由13个圆和连接它们圆心的线组成的几何图形,展示对称性和空间关系。首先绘制一个大圆,然后在大圆内部绘制12个同心圆,每个圆心与大圆的圆心连线。接着,将这些圆心连接起来,形成六边形结构。最后,在六边形中心绘制一个内接圆,完成整个图形的绘制。
以上提示语为根据原始绘图命令整理而来,仅供参考。