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尼罗河“新娘”几何构造：由圆弧与交点生成分段结构

尼罗河“新娘”几何构造：由圆弧与交点生成分段结构
几何画板及绘图内容加载中，请稍等……
2024-10-23 23:22
圆多边形解析几何几何作图函数图像
该范例展示如何通过一组圆、圆弧（CircumcircleArc）与多处交点构造出类似“尼罗河新娘”风格的分段几何图形。核心数学概念包括解析/几何作图中的圆与圆弧性质、由多圆交点形成的几何约束，以及线段与多边形的拼接表达。作图要点：从构造摘要提炼的 GeoGebra 命令主要为 Point（生成关键点 A1、B1、C、D 等）、CircumcircleArc（在已确定的圆/圆心条件下画圆弧）、Segment（连接形成线段与边）、Circle（建立圆）、Polygon（合成多边形轮廓）、Intersect（计算圆弧/直线/线段等之间的交点以确定后续构造）。适合中学到大学基础几何课程的学生使用，作为几何作图、几何构造与图形建模的演示案例，也适用于开展探究式学习与竞赛几何入门。

GeoGebra 命令及参数

  1. Point(f) → C
  2. Point(f) → D
  3. CircumcircleArc(H, I, L) → c
  4. Point(hr3) → M
  5. CircumcircleArc(L, E, M) → d
  6. CircumcircleArc(N, O, P) → e
  7. CircumcircleArc(Q, R, S) → k
  8. Segment(Q, T) → j
  9. CircumcircleArc(T, U, S) → p
  10. Segment(W_1, V) → l
  11. Point(hd1) → D_1
  12. Point(hd1) → H_1
  13. Point(hd1) → I_1
  14. Point(hd1) → K_1
  15. Point(hd1) → M_1
  16. Point(hd1) → N_1
  17. Point(hd1) → Q_1
  18. Point(hd1) → L_2
  19. Point(hd1) → M_2
  20. Point(hd1) → N_2
  21. Point(hd1) → O_2
  22. Segment(P_2, Q_2) → n
  23. Segment(R_2, S_2) → r
  24. Segment(T_2, U_2) → s
  25. Segment(S_2, T_2) → t
  26. Segment(R_2, U_2) → a
  27. CircumcircleArc(Q_2, V_2, W_2) → r_1
  28. Segment(A_3, B_3) → b
  29. Segment(C_3, D_3) → a_1
  30. CircumcircleArc(B_3, E_3, F_3) → q_2
  31. CircumcircleArc(D_3, G_3, H_3) → r_2
  32. CircumcircleArc(I_3, J_3, Q_2) → s_2
  33. CircumcircleArc(Z_2, K_3, L_3) → t_2
  34. CircumcircleArc(L_3, M_3, I_3) → c_3
  35. Segment(W, N_3) → b_1
  36. Segment(N_3, C_1) → c_1
  37. Segment(C_1, Z) → f_3
  38. Segment(Z, W) → g_3
  39. Segment(M, O_3) → h_3
  40. Segment(Q_3, R_3) → j_3
  41. Segment(R_3, S_3) → k_3
  42. CircumcircleArc(W_2, T_3, S_3) → d_3
  43. CircumcircleArc(G_1, D, U_3) → e_3
  44. Point(r_1) → V_3
  45. CircumcircleArc(V_3, W_3, R_3) → p_3
  46. Point(r_1) → Z_3
  47. Point(k_3) → B_4
  48. CircumcircleArc(Z_3, A_4, B_4) → q_3
  49. Segment(C_4, D_4) → l_3
  50. Point(hr1) → E_4
  51. CircumcircleArc(M, E_4, D_4) → r_3
  52. Segment(U_1, H_4) → m_3
  53. CircumcircleArc(I_4, J_4, K_4) → t_3
  54. Segment(K_4, H_4) → n_3
  55. Segment(I_4, L_4) → a_3
  56. CircumcircleArc(L_4, M_4, F) → c_4
  57. Circle(N_4, O_4) → d_4
  58. Point(h) → P_4
  59. CircumcircleArc(P_4, R_1, F) → e_4
  60. CircumcircleArc(F, Q_4, J_4) → f_4
  61. CircumcircleArc(U_3, R_4, C_4) → g_4
  62. Segment(V, R_2) → b_3
  63. Point(hd2) → E_5
  64. Point(hd2) → H_5
  65. Point(f_4) → P_5
  66. Point(hd1) → J_1
  67. Polygon(O_2, H_2, I_2, N_2) → q1, o_2, h_2, i_2, n_2
  68. Polygon(N_2, M_2, J_2, I_2) → q2, m, m_2, j_2, f_1
  69. Polygon(M_2, L_2, K_2, J_2) → q3, g_1, l_2, k_2, h_1
  70. Polygon(L_2, Q_1, G_2, K_2) → q4, i_1, q_1, g_2, j_1
  71. Polygon(Q_1, P_1, F_2, G_2) → q5, k_1, p_1, f_2, l_1
  72. Polygon(P_1, O_1, E_2, F_2) → q6, m_1, o_1, e_2, n_1
  73. Polygon(O_1, N_1, D_2, E_2) → q7, s_1, t_1, d_2, d_1
  74. Polygon(N_1, M_1, C_2, D_2) → q8, e_1, a_2, c_2, b_2
  75. Polygon(M_1, L_1, B_2, C_2) → q9, i_4, j_4, l_4, m_4
  76. Polygon(L_1, K_1, A_2, B_2) → q10, n_4, a_4, b_4, i_5
  77. Polygon(K_1, J_1, Z_1, A_2) → q11, j_5, l_5, z_1, m_5
  78. Polygon(J_1, I_1, T_1, Z_1) → q12, n_5, a_5, b_5, g_6
  79. Polygon(I_1, H_1, S_1, T_1) → q13, h_6, i_6, j_6, k_6
  80. Polygon(H_1, D_1, E_1, S_1) → q14, l_6, m_6, n_6, p_6
  81. Polygon(D_1, G_1, F_1, E_1) → q15, q_6, r_6, s_6, t_6
  82. Segment(Z_2, U_2) → a_6
  83. Segment(P_3, Q_3) → i
  84. Point(f) → B
  85. Point(f) → G_6
  86. Point(h) → I_6
  87. Point(h) → J_6
  88. Point(q) → K_6
  89. Point(hr4) → L_6
  90. Point(l_3) → M_6
  91. CircumcircleArc(K_6, L_6, M_6) → q_7
  92. CircumcircleArc(G, L_5, M_5) → s_3
  93. Point(hd2) → F_6
  94. CircumcircleArc(L_5, E_6, F_6) → h_4
  95. CircumcircleArc(E_6, N_6, O_6) → k_4
  96. CircumcircleArc(N_6, P_6, Q_6) → p_4
  97. Point(hd2) → S_6
  98. CircumcircleArc(P_6, R_6, S_6) → q_4
  99. CircumcircleArc(R_6, T_6, U_6) → r_4
  100. CircumcircleArc(T_6, V_6, W_6) → s_4
  101. Point(f) → Z_6
  102. Point(f) → A_7
  103. CircumcircleArc(V_6, Z_6, A_7) → t_4
  104. Point(s_3) → H_7
  105. Point(h_4) → I_7
  106. CircumcircleArc(H_7, B_7, I_7) → c_5
  107. Point(k_4) → J_7
  108. CircumcircleArc(I_7, C_7, J_7) → d_5
  109. CircumcircleArc(J_7, D_7, P_6) → e_5
  110. Point(r_4) → G_7
  111. CircumcircleArc(P_6, E_7, G_7) → f_5
  112. CircumcircleArc(G_7, F_7, V_6) → g_5
  113. Point(g_5) → K_7
  114. CircumcircleArc(K_7, L_7, Z_6) → h_5
  115. CircumcircleArc(B_7, M_7, C_7) → k_5
  116. CircumcircleArc(C_7, N_7, D_7) → p_5
  117. CircumcircleArc(D_7, O_7, E_7) → q_5
  118. CircumcircleArc(E_7, P_7, F_7) → r_5
  119. CircumcircleArc(F_7, Q_7, L_7) → s_5
  120. Intersect(c_4, e_4, 1) → R_7
  121. CircumcircleArc(R_7, S_7, B_7) → t_5
  122. CircumcircleArc(R_7, T_7, M_7) → c_6
  123. CircumcircleArc(M_7, U_7, N_7) → d_6
  124. CircumcircleArc(N_7, V_7, O_7) → e_6
  125. CircumcircleArc(O_7, W_7, P_7) → f_6
  126. CircumcircleArc(T_7, A_8, U_7) → d_7
  127. CircumcircleArc(U_7, B_8, V_7) → e_7
  128. CircumcircleArc(V_7, C_8, W_7) → f_7
  129. CircumcircleArc(W_7, D_8, Z_7) → g_7
  130. CircumcircleArc(A_8, F_8, B_8) → h_7
  131. CircumcircleArc(B_8, G_8, C_8) → k_7
  132. CircumcircleArc(C_8, H_8, D_8) → p_7
  133. CircumcircleArc(F_8, I_8, G_8) → r_7
  134. CircumcircleArc(G_8, J_8, H_8) → s_7
  135. CircumcircleArc(H_8, K_8, Z_7) → t_7
  136. CircumcircleArc(P_4, L_8, F_8) → c_8
  137. CircumcircleArc(L_8, M_8, I_8) → d_8
  138. CircumcircleArc(R_1, N_8, A_8) → e_8
  139. Point(r_7) → P_8
  140. CircumcircleArc(P_8, O_8, J_8) → f_8
  141. CircumcircleArc(J_8, Q_8, K_8) → g_8
  142. Point(h) → S_8
  143. CircumcircleArc(S_8, R_8, O_8) → h_8
  144. CircumcircleArc(O_8, T_8, Q_8) → k_8
  145. Point(h) → U_8
  146. CircumcircleArc(R_8, U_8, T_8) → p_8
  147. CircumcircleArc(P_7, V_8, Q_7) → c_7
  148. CircumcircleArc(K_8, E_8, Q_7) → q_8
  149. Segment(K_4, O_2) → i_3
  150. Circle(W_8, Z_8) → r_8

AI 绘图提示语参考

画一个由多个圆、圆弧和线段组成的几何图形，首先确定几个关键点，然后绘制几个圆的圆弧，通过计算这些圆弧的交点来得到新的点，接着用线段连接这些点形成多边形，最后将这些部分组合成一个连贯的整体，展示圆和圆弧之间的关系以及如何通过交点来构建复杂的几何形状。
以上提示语为根据原始绘图命令整理而来，仅供参考。