风筝的几何构造 by Mr Duncan

风筝的几何构造 by Mr Duncan
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2020-01-10 23:44
①本范例演示风筝形状的几何构造及其相关性质;②涉及的核心数学概念包括多边形、角、圆、切线、中点、垂线等;③作图要点提炼自构造摘要,使用了Circle(圆)、Tangent(切线)、Intersect(交点)、Segment(线段)、Line(直线)、Midpoint(中点)、OrthogonalLine(垂线)、Angle(角度)等GeoGebra命令;④适合高中阶段学习几何作图、解析几何及多边形性质的学生使用。

GeoGebra 命令及参数

  1. Circle(B_2, 21.43318565057029) → d
  2. Circle(C_2, 16.02850007793855) → e
  3. Circle(D_2, 21.97966183159147) → f
  4. Circle(E_2, 19.85274664077369) → g
  5. Circle(F_2, 8.503832872485338) → h
  6. Tangent(H, d) → k, l
  7. Tangent(I, f) → m, n
  8. Tangent(L, g) → p, q
  9. Tangent(D, e) → r, s
  10. Tangent(K, h) → t, a
  11. Intersect(d, l, 1) → M
  12. Intersect(d, k, 1) → N
  13. Intersect(h, a, 1) → Q
  14. Intersect(h, t, 1) → R
  15. Intersect(e, s, 1) → C
  16. Intersect(e, r, 1) → A
  17. Intersect(f, m, 1) → U
  18. Intersect(f, n, 1) → V
  19. Intersect(g, q, 1) → W
  20. Intersect(g, p, 1) → Z
  21. Segment(U, I) → b
  22. Segment(I, V) → f_1
  23. Segment(L, Z) → g_1
  24. Segment(W, L) → h_1
  25. Segment(K, R) → i_1
  26. Segment(K, Q) → j_1
  27. Segment(D, C) → k_1
  28. Segment(H, N) → l_1
  29. Segment(H, M) → m_1
  30. Segment(A, D) → q_1
  31. Segment(B_2, N) → t_1
  32. Segment(B_2, M) → a_1
  33. Segment(C_2, A) → b_1
  34. Segment(C_2, C) → c_1
  35. Segment(F_2, Q) → d_1
  36. Segment(F_2, R) → e_1
  37. Segment(E_2, W) → f_2
  38. Segment(E_2, Z) → g_2
  39. Segment(D_2, V) → h_2
  40. Segment(D_2, U) → i_2
  41. Line(A, k_1) → j_2
  42. Midpoint(A, D) → A_1
  43. OrthogonalLine(A_1, q_1) → k_2
  44. Intersect(j_2, k_2) → B
  45. Segment(D, B) → l_2
  46. Segment(B, A) → m_2
  47. Angle(N, H, M) → α
  48. Angle(M, B_2, N) → β
  49. Angle(U, I, V) → γ
  50. Angle(A, D, C) → δ
  51. Segment(E_2, L) → n_2
  52. Intersect(g, n_2, 1) → C_1
  53. OrthogonalLine(C_1, n_2) → p_2
  54. Intersect(p_2, h_1) → D_1
  55. Segment(C_1, D_1) → q_2
  56. Intersect(p_2, g_1) → E_1
  57. Segment(C_1, E_1) → r_2
  58. Angle(W, E_2, C_1) → ε
  59. Line(R, j_1) → s_2
  60. Line(Q, i_1) → t_2
  61. Line(F_2, K) → a_2
  62. OrthogonalLine(K, a_2) → b_2
  63. Intersect(s_2, b_2) → E
  64. Intersect(t_2, b_2) → F
  65. Segment(R, E) → c_2
  66. Segment(E, F) → d_2
  67. Segment(F, Q) → e_2
  68. Angle(K, F, Q) → ζ
  69. Angle(H, M, B_2) → η
  70. Angle(B_2, N, H) → θ

AI 绘图提示语参考

画一个风筝的几何构造图,包含三个圆,分别以不同点为圆心,画出圆与圆的切线,再求切线的交点得到风筝的顶点,连接这些顶点形成风筝的边,并标注出风筝的对角线和中点,最后画出对角线的中垂线,展示风筝的对称性和相关角度。
以上提示语为根据原始绘图命令整理而来,仅供参考。