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Sean Jackson 几何构造：线段、圆与正交线的综合作图

Sean Jackson 几何构造：线段、圆与正交线的综合作图
几何画板及绘图内容加载中，请稍等……
2016-03-09 23:18
圆角解析几何变换几何作图
该范例展示了一个由点、线段、直线、圆、正交线、中点、镜像等基本几何元素构成的复杂构造图形，演示了如何通过GeoGebra命令逐步构建包含角度、距离测量和文本标注的几何关系网络。核心数学概念涉及欧几里得几何中的基本作图（如作中点、垂线、镜像）、角度与距离的度量，以及线性回归、参数曲线、正弦函数、随机变量和球体等扩展主题的潜在联系。作图要点包括使用Segment、Line、Point、Intersect、Angle、Distance、Circle、OrthogonalLine、Midpoint、Mirror等命令，并创建了多个点（A、B、C、D、E、F、G、H、I、J、K）、线段（a、b、c、d、e、f、h、g、i、j、k、q、l、m、n、p、r）、角度（α、β、γ、δ）以及距离文本（distanceAF、TextAF等）对象。适合中学及以上学段用于几何作图练习、动态探索几何性质，或作为教师演示复杂构造步骤的示例。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Line(C, a) → b
  3. Point(b) → D
  4. Segment(B, D) → c
  5. Line(A, c) → d
  6. Intersect(b, d) → E
  7. Segment(D, E) → e
  8. Segment(A, E) → f
  9. Angle(B, A, E) → α
  10. Angle(A, E, D) → β
  11. Angle(E, D, B) → γ
  12. Angle(D, B, A) → δ
  13. Segment(E, B) → h
  14. Segment(A, D) → g
  15. Intersect(h, g) → F
  16. Distance(A, F) → distanceAF
  17. Distance(F, E) → distanceFE
  18. Distance(D, F) → distanceDF
  19. Distance(F, B) → distanceFB
  20. Segment(G, H) → i
  21. Circle(G, H) → k
  22. Point(k) → J
  23. Segment(G, J) → j
  24. Circle(G, H) → q
  25. Line(J, i) → l
  26. Line(H, j) → m
  27. Intersect(l, m) → K
  28. Segment(J, K) → n
  29. Segment(K, H) → p
  30. Segment(H, J) → r
  31. Segment(G, K) → s
  32. Intersect(r, s) → L
  33. Angle(G, L, J) → ε
  34. Angle(K, J, L) → ζ
  35. Angle(L, J, G) → η
  36. Angle(J, G, L) → θ
  37. Angle(L, G, H) → ι
  38. Angle(G, H, L) → κ
  39. Angle(L, H, K) → λ
  40. Angle(H, K, L) → μ
  41. Angle(L, K, J) → ν
  42. Segment(M, N) → t
  43. Line(O, t) → a_1
  44. OrthogonalLine(N, t) → b_1
  45. OrthogonalLine(M, t) → c_1
  46. Intersect(a_1, c_1) → P
  47. Intersect(a_1, b_1) → Q
  48. Segment(N, Q) → d_1
  49. Segment(Q, P) → e_1
  50. Segment(P, M) → f_1
  51. Angle(M, N, Q) → ξ
  52. Angle(N, Q, P) → ο
  53. Angle(Q, P, M) → ρ
  54. Angle(P, M, N) → σ
  55. Segment(N, P) → g_1
  56. Segment(Q, M) → h_1
  57. Segment(R, S) → i_1
  58. Circle(R, S) → k_1
  59. OrthogonalLine(R, i_1) → j_1
  60. Circle(R, S) → p_1
  61. Intersect(p_1, j_1, 1) → T
  62. Line(T, i_1) → l_1
  63. OrthogonalLine(S, i_1) → m_1
  64. Intersect(l_1, m_1) → U
  65. Intersect(j_1, l_1) → V
  66. Segment(V, R) → n_1
  67. Segment(U, S) → q_1
  68. Segment(V, U) → r_1
  69. Segment(R, U) → s_1
  70. Segment(S, V) → t_1
  71. Intersect(s_1, t_1) → W
  72. Angle(U, W, S) → τ
  73. Angle(S, W, R) → υ
  74. Angle(R, W, V) → ϕ
  75. Segment(Z, A_1) → a_2
  76. Line(B_1, a_2) → b_2
  77. Point(b_2) → C_1
  78. Segment(Z, C_1) → c_2
  79. Segment(A_1, B_1) → d_2
  80. Segment(C_1, B_1) → e_2
  81. Midpoint(c_2) → D_1
  82. Midpoint(d_2) → E_1
  83. Segment(D_1, E_1) → f_2
  84. Segment(F_1, G_1) → g_2
  85. Line(H_1, g_2) → h_2
  86. Point(h_2) → I_1
  87. Segment(F_1, I_1) → i_2
  88. Midpoint(g_2) → J_1
  89. OrthogonalLine(J_1, g_2) → j_2
  90. Mirror(F_1, j_2) → K_1
  91. Mirror(I_1, j_2) → L_1
  92. Segment(K_1, L_1) → k_2
  93. Segment(I_1, L_1) → l_2
  94. Segment(P_1, Q_1) → p_2
  95. Midpoint(p_2) → R_1
  96. OrthogonalLine(R_1, p_2) → q_2
  97. Point(q_2) → O_1
  98. Segment(P_1, O_1) → n_2
  99. Mirror(P_1, q_2) → S_1
  100. Mirror(O_1, q_2) → T_1
  101. Segment(S_1, T_1) → r_2
  102. Point(q_2) → U_1
  103. Segment(Q_1, U_1) → s_2
  104. Mirror(Q_1, q_2) → V_1
  105. Mirror(U_1, q_2) → W_1
  106. Segment(V_1, W_1) → t_2
  107. Segment(O_1, U_1) → a_3
  108. Intersect(p_2, a_3) → Z_1
  109. Angle(Q_1, Z_1, O_1) → ψ
  110. Angle(U_1, P_1, O_1) → χ
  111. Angle(O_1, Q_1, U_1) → α_1
  112. Angle(V, R, S) → ω
  113. Angle(S, U, V) → β_1
  114. Angle(W, V, R) → γ_1
  115. Angle(W, S, U) → δ_1
  116. Segment(F_1, L_1) → b_3
  117. Segment(I_1, G_1) → c_3