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图形拟合与构造

图形拟合与构造
几何画板及绘图内容加载中，请稍等……
2016-06-02 03:40
多边形解析几何几何作图
①本范例演示了如何通过点、线段、圆等基本元素构造等边三角形、中位线、正方形等几何图形，并探讨其相互关系；②涉及的核心数学概念包括线段、等边三角形、中位线、正方形、解析几何；③作图要点提炼自构造摘要，使用了Point（点）、Segment（线段）、Circle（圆）、OrthogonalLine（垂线）、Intersect（交点）、Polygon（多边形）、Midpoint（中点）等GeoGebra命令与对象；④适合高中数学教学，用于几何作图练习与概念理解。

GeoGebra 命令及参数

  1. Point(Circle[A, r]) → B
  2. Segment(A, B) → f
  3. Circle(A, r) → c
  4. Circle(A, (2 * r)) → d
  5. Circle(A, (3 * r)) → e
  6. OrthogonalLine(A, f) → g
  7. Intersect(c, g, 2) → C
  8. Intersect(d, g, 2) → D
  9. Intersect(e, g, 2) → E
  10. OrthogonalLine(C, g) → h
  11. OrthogonalLine(D, g) → i
  12. OrthogonalLine(E, g) → j
  13. Circle(C, r) → k
  14. Circle(C, (2 * r)) → p
  15. Intersect(k, h, 2) → F
  16. Intersect(k, h, 1) → I
  17. Intersect(p, h, 1) → J
  18. OrthogonalLine(F, h) → l
  19. OrthogonalLine(I, h) → m
  20. OrthogonalLine(J, h) → n
  21. Intersect(n, i) → G
  22. Intersect(j, m) → H
  23. Intersect(i, m) → K
  24. Intersect(i, l) → L
  25. Polygon(A, C, I, B, F, L, D, E, H, K, G, J) → poly1, a, j_1, i_1, b, c_1, f_1, l_1, d_1, e_1, h_1, k_1, g_1
  26. Segment(C, G) → q
  27. OrthogonalLine(C, q) → s
  28. Intersect(s, l_1) → M
  29. Intersect(s, f) → N
  30. Polygon(M, C, G, K, H, E, D) → poly2, m_1, c_2, g_2, k_2, h_2, e_2, d_2
  31. Polygon(N, C, G, J, I, B) → poly3, n_1, c_3, g_3, j_2, i_2, b_1
  32. Polygon(C, A, N) → poly4, n_2, c_4, a_1
  33. Polygon(L, F, C, M) → poly5, l_2, f_2, c_5, m_2
  34. Point(Circle[P, q]) → Q
  35. Segment(P, Q) → t
  36. OrthogonalLine(P, t) → p_1
  37. Circle(P, m_1) → q_1
  38. Intersect(q_1, p_1, 2) → R
  39. Segment(R, P) → r_1
  40. Segment(R, Q) → s_1
  41. OrthogonalLine(P, s_1) → t_1
  42. Intersect(t_1, s_1) → S
  43. Circle(S, r) → p_2
  44. Intersect(p_2, s_1, 1) → T
  45. Polygon(S, T, 4) → poly6, q_2, r_2, s_2, t_2, U, V
  46. Polygon(P, R, S, V, U, T, Q) → poly7, p_3, r_3, s_3, v, u, t_3, q_3
  47. Circle(W, c_3) → d_3
  48. Point(d_3) → Z
  49. Segment(W, Z) → a_2
  50. OrthogonalLine(W, a_2) → b_2
  51. Circle(W, n_1) → e_3
  52. Intersect(e_3, b_2, 1) → A_1
  53. Segment(W, A_1) → f_3
  54. Midpoint(a_2) → B_1
  55. Circle(B_1, W) → h_3
  56. Circle(W, (2 * r)) → k_3
  57. Intersect(h_3, k_3, 1) → C_1
  58. Midpoint(W, C_1) → D_1
  59. Segment(W, C_1) → i_3
  60. OrthogonalLine(D_1, i_3) → j_3
  61. Circle(D_1, r) → d_4
  62. Intersect(d_4, j_3, 1) → E_1
  63. Polygon(W, Z, C_1, D_1, E_1, A_1) → poly8, w, z_1, c_6, d_5, e_4, a_3
  64. Point(Circle[F_1, r]) → G_1
  65. Segment(F_1, G_1) → l_3
  66. OrthogonalLine(G_1, l_3) → m_3
  67. Circle(G_1, r) → f_4
  68. Intersect(f_4, m_3, 2) → H_1
  69. Segment(L, M) → n_3
  70. OrthogonalLine(F_1, l_3) → b_3
  71. Circle(F_1, n_3) → g_4
  72. Intersect(g_4, b_3, 2) → I_1
  73. Segment(I_1, H_1) → h_4
  74. Polygon(I_1, F_1, G_1, H_1) → poly9, i_4, f_5, g_5, h_5
  75. Point(Circle[J_1, r]) → K_1
  76. Segment(J_1, K_1) → j_4
  77. OrthogonalLine(K_1, j_4) → k_4
  78. Segment(A, N) → l_4
  79. Circle(K_1, Segment[A, N]) → p_4
  80. Intersect(p_4, k_4, 2) → L_1
  81. Polygon(J_1, L_1, K_1) → poly10, k_5, j_5, l_5
  82. Point(Circle[M_1, c_3]) → N_1
  83. Segment(M_1, N_1) → m_4
  84. Polygon(M_1, N_1, 4) → poly11, n_4, q_4, r_4, s_4, O_1, P_1