积极 AI Logo 积极 AI

Shearer Action 4! 几何作图与对称性探索

Shearer Action 4! 几何作图与对称性探索
几何画板及绘图内容加载中，请稍等……
2019-05-04 10:08
圆向量几何作图
该范例演示了通过动态几何工具解决几何问题的方法。核心数学概念包括圆、向量、重心或重心坐标、勾股定理等。作图要点涉及使用GeoGebra命令如Ray、Point、Circle、OrthogonalLine等构建图形。适合中学几何学习者，用于理解几何变换与对称性。

GeoGebra 命令及参数

  1. Ray(A, A + (0, 1)) → f
  2. Point(f) → B
  3. Circle(B, A) → c
  4. Ray(A, A + (2, 0)) → h
  5. Point(h) → C
  6. Point(c) → F
  7. Segment(B, F) → j
  8. OrthogonalLine(F, j) → l
  9. Line(B, F) → m
  10. Intersect(g, l) → G
  11. Angle(C, G, F) → α
  12. Rotate(C, α / 2, G) → C'
  13. Ray(G, C') → n
  14. Intersect(m, n) → H
  15. Circle(H, F) → d
  16. Intersect(d, g, 1) → D
  17. CircleArc(B, F, A) → e
  18. CircleArc(H, D, F) → k
  19. Point(e) → E
  20. Point(k) → I
  21. Angle(A, E, F) → β
  22. Angle(F, I, D) → γ
  23. Midpoint(A, D) → J
  24. Ray(J, J - (0, 1)) → i
  25. Point(i) → K
  26. Angle(A, J, K) → ε
  27. Point(g) → L
  28. Point(g) → M
  29. Angle(M, D, H) → ζ
  30. Angle(B, A, L) → η
  31. Segment(H, D) → q
  32. Segment(B, A) → p
  33. Dilate(B, If[0 < b ≤ 1, 1 - b, 0], A) → B'
  34. Dilate(H, If[0 < b ≤ 1, 1 - b, 0], D) → H'
  35. Segment(B, B') → r
  36. Segment(H, H') → s
  37. Dilate(E, If[1 < b ≤ 2, 2 - b, 0], A) → E'
  38. Dilate(E, If[1 < b ≤ 2, 2 - b, 0], F) → E'_1
  39. Dilate(I, If[1 < b ≤ 2, 2 - b, 0], F) → I'
  40. Dilate(I, If[1 < b ≤ 2, 2 - b, 0], D) → I'_1
  41. Segment(E, E') → t
  42. Segment(E, E'_1) → f_1
  43. Segment(I, I') → g_1
  44. Segment(I, I'_1) → h_1
  45. Min({Distance[E, A], Distance[E, F], Distance[I, F], Distance[I, D]}) → o
  46. Circle(E, (0.3 * o)) → c_1
  47. Circle(I, (0.3 * o)) → d_1
  48. Intersect(c_1, t, 1) → N
  49. Intersect(d_1, g_1, 1) → O
  50. Rotate(O, If[2 < b ≤ 3, ((b - 2) * γ), γ], I) → O'
  51. Rotate(N, If[2 < b ≤ 3, ((b - 2) * β), β], E) → N'
  52. CircleSector(E, N, N') → e_1
  53. CircleSector(I, O, O') → k_1
  54. Line(E, i) → i_1
  55. Point(i_1) → P
  56. Angle(P, E, A) → θ
  57. Semicircle(E, J) → p_1
  58. Rotate(E, If[4 < b ≤ 5, ((-(b - 4)) * π), (-π)], Midpoint[E, J]) → E'_2
  59. Vector(E, E'_2) → u
  60. Translate(e_1, u) → q_1
  61. Rotate(q_1, If[4 < b ≤ 5, ((b - 4) * ((2 * π) - θ)), (2 * π) - θ], E'_2) → r_1
  62. Semicircle(J, I) → s_1
  63. Dilate(I, If[5 < b ≤ 6, 6 - b, 0], J) → I'_2
  64. Vector(I, I'_2) → v
  65. Translate(k_1, v) → t_1
  66. Line(I, g) → j_1
  67. Point(j_1) → Q
  68. Angle(D, I, Q) → κ
  69. Rotate(t_1, If[5 < b ≤ 6, ((-(b - 5)) * ((2 * π) - κ)), κ - (2 * π)], I'_2) → c_2