四边形构造 by Taylor Rish

四边形构造 by Taylor Rish
几何画板及绘图内容加载中,请稍等……
2016-11-24 02:38
这个范例演示了四边形的构造方法。涉及的核心数学概念包括几何构造、三角函数和变换。通过使用GeoGebra命令如Segment、Circle、Intersect等,可以构造出各种类型的四边形。适合初中和高中学生学习几何作图。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Circle(C, Segment[C, D]) → c
  3. Intersect(c, f, 1) → E
  4. Circle(E, Segment[C, D]) → d
  5. Intersect(d, f, 1) → F
  6. Circle(F, Segment[C, D]) → e
  7. Intersect(c, e, 1) → G
  8. Segment(C, G) → g
  9. Segment(G, F) → h
  10. Segment(E, C) → i
  11. Segment(F, E) → j
  12. Segment(E, F) → k
  13. Segment(E, F) → l
  14. Point(g) → H
  15. Point(h) → I
  16. Point(f) → J
  17. Point(i) → K
  18. Angle(K, C, H) → α
  19. Angle(H, G, I) → β
  20. Angle(I, F, J) → γ
  21. Angle(J, E, K) → δ
  22. Segment(G, E) → m
  23. Segment(C, F) → n
  24. Intersect(m, n) → L
  25. Angle(C, L, E) → ε
  26. Angle(F, L, G) → ζ
  27. Angle(G, L, C) → η
  28. Angle(E, L, F) → θ
  29. Segment(L, E) → p
  30. Segment(L, G) → q
  31. Segment(F, L) → r
  32. Segment(C, L) → s
  33. Segment(M, N) → t
  34. Segment(N, O) → a
  35. Point(t) → P
  36. Circle(N, Segment[N, P]) → c_1
  37. Intersect(c_1, a, 1) → Q
  38. Circle(Q, Segment[N, O]) → d_1
  39. Circle(P, Segment[O, N]) → e_1
  40. Circle(M, Segment[M, N]) → f_1
  41. Circle(N, Segment[N, M]) → g_1
  42. Point(g_1) → S
  43. Segment(N, S) → h_1
  44. Circle(S, Segment[M, N]) → k_1
  45. Intersect(f_1, k_1, 1) → T
  46. Segment(T, S) → i_1
  47. Segment(T, M) → j_1
  48. Angle(T, S, N) → ι
  49. Segment(S, N) → l_1
  50. Angle(S, N, P) → κ
  51. Angle(P, M, T) → λ
  52. Angle(M, T, S) → μ
  53. Segment(T, N) → b
  54. Segment(S, M) → m_1
  55. Intersect(b, m_1) → R
  56. Angle(T, R, M) → ν
  57. Angle(M, R, N) → ξ
  58. Angle(N, R, S) → ο
  59. Angle(S, R, T) → ρ
  60. Segment(T, R) → n_1
  61. Segment(R, N) → p_1
  62. Segment(S, R) → q_1
  63. Segment(R, M) → r_1
  64. Segment(U, V) → s_1
  65. Segment(U, W) → t_1
  66. Point(s_1) → Z
  67. Circle(U, Segment[Z, U]) → c_2
  68. Intersect(c_2, t_1, 1) → A_1
  69. Circle(Z, Segment[Z, A_1]) → d_2
  70. Circle(A_1, Segment[Z, A_1]) → e_2
  71. Intersect(d_2, e_2, 2) → B_1
  72. Segment(U, B_1) → a_1
  73. Segment(W, B_1) → b_1
  74. Segment(B_1, C_1) → f_2
  75. Segment(W, D_1) → g_2
  76. Intersect(f_2, g_2) → E_1
  77. Segment(W, E_1) → h_2
  78. Segment(E_1, B_1) → i_2
  79. Angle(U, W, E_1) → σ
  80. Angle(B_1, U, W) → τ
  81. Rotate(W, 90°, E_1) → W'
  82. Angle(W, E_1, W') → υ
  83. Rotate(E_1, 90°, B_1) → F_1
  84. Angle(E_1, B_1, F_1) → ϕ
  85. Segment(F_1, U) → j_2
  86. Segment(E_1, U) → k_2
  87. Intersect(b_1, k_2) → G_1
  88. Segment(H_1, I_1) → l_2
  89. Circle(I_1, Segment[H_1, I_1]) → p_2
  90. Circle(H_1, Segment[I_1, H_1]) → q_2
  91. Intersect(p_2, q_2, 2) → J_1
  92. Segment(J_1, K_1) → m_2
  93. Segment(J_1, H_1) → n_2
  94. Segment(H_1, K_1) → r_2
  95. Segment(J_1, I_1) → s_2
  96. Segment(I_1, K_1) → t_2
  97. Intersect(l_2, m_2) → L_1
  98. Angle(J_1, L_1, H_1) → χ
  99. Angle(I_1, L_1, J_1) → ψ
  100. Angle(K_1, L_1, I_1) → ω
  101. Angle(H_1, L_1, K_1) → α_1
  102. Angle(K_1, H_1, J_1) → β_1
  103. Angle(J_1, I_1, K_1) → γ_1
  104. Angle(L_1, K_1, H_1) → δ_1
  105. Angle(I_1, K_1, L_1) → ε_1
  106. Angle(H_1, J_1, L_1) → ζ_1
  107. Angle(L_1, J_1, I_1) → η_1
  108. Segment(M_1, N_1) → a_2
  109. Segment(O_1, P_1) → b_2
  110. Segment(P_1, N_1) → f_3
  111. Segment(O_1, M_1) → g_3
  112. Angle(M_1, O_1, P_1) → θ_1
  113. Angle(O_1, P_1, N_1) → ι_1
  114. Angle(N_1, M_1, O_1) → κ_1
  115. Angle(P_1, N_1, M_1) → λ_1
  116. Segment(O_1, N_1) → h_3
  117. Segment(M_1, P_1) → i_3
  118. Segment(Q_1, R_1) → j_3
  119. Line(S_1, j_3) → k_3
  120. Segment(Q_1, S_1) → l_3
  121. Line(R_1, l_3) → m_3
  122. Intersect(k_3, m_3) → T_1
  123. Segment(R_1, T_1) → n_3
  124. Segment(T_1, S_1) → p_3
  125. Angle(Q_1, R_1, T_1) → μ_1
  126. Angle(R_1, T_1, S_1) → ν_1
  127. Angle(T_1, S_1, Q_1) → ξ_1
  128. Angle(S_1, Q_1, R_1) → ο_1
  129. Segment(R_1, S_1) → q_3
  130. Segment(T_1, Q_1) → r_3
  131. Intersect(q_3, r_3) → U_1
  132. Segment(Q_1, U_1) → s_3
  133. Segment(U_1, T_1) → t_3
  134. Segment(R_1, U_1) → a_3
  135. Segment(U_1, S_1) → b_3

AI 绘图提示语参考

绘制一个四边形,使用点C和D作为对角线的端点,通过构造线段、圆和交点来确定其他顶点E、F、G和H。接着,通过角的测量和线段的连接,构造出四边形的内部结构,包括角α、β、γ和δ。最后,通过线段和圆的交点,进一步完善四边形的构造,确保所有边和角都符合几何要求。
以上提示语为根据原始绘图命令整理而来,仅供参考。