五角星构造

五角星构造
几何画板及绘图内容加载中,请稍等……
2015-02-03 22:44
①本范例演示五角星的绘制方法;②涉及核心数学概念包括多边形构造、线段与圆的交点计算;③作图要点:使用Segment(线段)、Circle(圆)、Polygon(多边形)、Midpoint(中点)、Line(直线)、Intersect(交点)等GeoGebra命令;④适合初中及以上学生学习几何作图和基础图形构造。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Circle(A, B) → c
  3. Circle(B, A) → d
  4. Polygon(B, A, 4) → poly1, b, e, f, g, C, D
  5. Midpoint(A, B) → E
  6. Circle(E, C) → h
  7. Line(A, B) → i
  8. Intersect(h, i, 1) → F
  9. Intersect(h, i, 2) → G
  10. Circle(B, G) → k
  11. Circle(A, F) → p
  12. Intersect(k, p, 2) → H
  13. Intersect(d, p, 1) → I
  14. Intersect(c, k, 2) → J
  15. Segment(H, I) → j
  16. Segment(I, B) → l
  17. Segment(A, J) → m
  18. Segment(J, H) → n
  19. Intersect(i, a) → K
  20. Intersect(j, i) → L
  21. Intersect(m, j) → M
  22. Intersect(m, l) → N
  23. Intersect(n, l) → O
  24. Intersect(i, a) → P
  25. Intersect(n, i) → Q
  26. Segment(L, N) → q
  27. Segment(N, Q) → r
  28. Segment(Q, M) → s
  29. Segment(M, O) → t
  30. Segment(O, L) → a_1
  31. Intersect(q, s) → R
  32. Intersect(q, t) → S
  33. Intersect(t, r) → T
  34. Intersect(r, a_1) → U
  35. Intersect(a_1, s) → V
  36. Segment(V, S) → b_1
  37. Segment(S, U) → c_1
  38. Segment(U, R) → d_1
  39. Segment(R, T) → e_1
  40. Segment(T, V) → f_1
  41. Intersect(b_1, d_1) → W
  42. Intersect(b_1, e_1) → Z
  43. Intersect(c_1, e_1) → A_1
  44. Intersect(c_1, f_1) → B_1
  45. Intersect(d_1, f_1) → C_1
  46. Segment(W, A_1) → g_1
  47. Segment(A_1, C_1) → h_1
  48. Segment(C_1, Z) → i_1
  49. Segment(Z, B_1) → j_1
  50. Segment(B_1, W) → k_1
  51. Intersect(i_1, k_1) → D_1
  52. Intersect(g_1, i_1) → E_1
  53. Intersect(g_1, j_1) → F_1
  54. Intersect(h_1, j_1) → G_1
  55. Intersect(h_1, k_1) → H_1
  56. Segment(D_1, F_1) → l_1
  57. Segment(F_1, H_1) → m_1
  58. Segment(H_1, E_1) → n_1
  59. Segment(E_1, G_1) → p_1
  60. Segment(G_1, D_1) → q_1
  61. Intersect(l_1, n_1) → I_1
  62. Intersect(l_1, p_1) → J_1
  63. Intersect(m_1, p_1) → K_1
  64. Intersect(m_1, q_1) → L_1
  65. Intersect(n_1, q_1) → M_1
  66. Segment(I_1, K_1) → r_1
  67. Segment(K_1, M_1) → s_1
  68. Segment(M_1, J_1) → t_1
  69. Segment(J_1, L_1) → a_2
  70. Segment(L_1, I_1) → b_2
  71. Intersect(t_1, b_2) → N_1
  72. Intersect(r_1, t_1) → O_1
  73. Intersect(r_1, a_2) → P_1
  74. Intersect(s_1, a_2) → Q_1
  75. Intersect(s_1, b_2) → R_1
  76. Segment(N_1, P_1) → c_2
  77. Segment(P_1, R_1) → d_2
  78. Segment(R_1, O_1) → e_2
  79. Segment(O_1, Q_1) → f_2
  80. Segment(Q_1, N_1) → g_2

AI 绘图提示语参考

画一个五角星,首先画出两条线段和两个圆,然后利用这些圆和线段相交得到五个顶点,连接这些顶点构成一个正五边形,接着找到线段的中点并以此为圆心画圆,再与之前画的圆相交得到新的点,最后连接这些新点形成五角星的内部装饰线,最终呈现出一个完整的五角星图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。