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正方形中的圆

正方形中的圆
几何画板及绘图内容加载中，请稍等……
2016-01-13 04:28
圆多边形函数
本范例演示正方形中圆的复合面积。涉及的核心数学概念包括圆、正方形和二次函数。通过使用GeoGebra命令如Intersect、Circle、Polygon等进行几何作图。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 4) → c
  3. Intersect(c, xAxis, 2) → C
  4. Polygon(A, C, 4) → poly1, a, b, d, e, B, D
  5. Circle(A, f) → g
  6. Intersect(g, a, 1) → E
  7. Intersect(g, e, 1) → F
  8. Circle(E, A) → k
  9. Intersect(k, a, 2) → H
  10. Circle(F, A) → q
  11. Intersect(q, e, 2) → I
  12. Circle(I, F) → r
  13. Intersect(r, e, 2) → J
  14. Circle(H, E) → s
  15. Intersect(s, a, 2) → K
  16. Intersect(k, q, 2) → G
  17. Circle(G, E) → h
  18. Circle(J, I) → p
  19. Circle(K, H) → t
  20. Intersect(p, e, 2) → L
  21. Intersect(t, a, 2) → M
  22. Circle(L, J) → c_1
  23. Circle(M, K) → d_1
  24. Intersect(c_1, e, 2) → N
  25. Intersect(d_1, a, 2) → O
  26. Circle(N, L) → e_1
  27. Circle(O, M) → f_1
  28. OrthogonalLine(G, e) → i
  29. Intersect(t, i, 1) → P
  30. Intersect(t, i, 1) → Q
  31. Circle(P, K) → g_1
  32. OrthogonalLine(E, i) → j
  33. Intersect(p, j, 1) → R
  34. Circle(R, J) → h_1
  35. Intersect(e_1, j, 1) → S
  36. Circle(S, N) → k_1
  37. Intersect(f_1, i, 1) → T
  38. OrthogonalLine(I, e) → l
  39. OrthogonalLine(H, a) → m
  40. Intersect(h_1, m, 1) → U
  41. Intersect(g_1, l, 1) → V
  42. Circle(T, O) → p_1
  43. Intersect(p_1, l, 1) → W
  44. Intersect(k_1, m, 1) → Z
  45. Line(P, V) → a_1
  46. Line(T, W) → b_1
  47. Line(R, U) → i_1
  48. Line(S, Z) → j_1
  49. OrthogonalLine(L, e) → l_1
  50. OrthogonalLine(M, a) → m_1
  51. Intersect(a_1, j_1) → A_1
  52. Intersect(a_1, i_1) → B_1
  53. Intersect(b_1, i_1) → C_1
  54. Intersect(j_1, b_1) → D_1
  55. Circle(A_1, Z) → q_1
  56. Intersect(m_1, j_1) → E_1
  57. Intersect(i_1, m_1) → F_1
  58. Circle(D_1, E_1) → r_1
  59. Circle(C_1, W) → s_1
  60. Circle(B_1, U) → t_1
  61. Intersect(e_1, e, 2) → G_1
  62. Intersect(f_1, a, 2) → H_1
  63. Circle(G_1, N) → c_2
  64. Circle(H_1, O) → d_2
  65. Intersect(c_2, e, 2) → I_1
  66. Intersect(d_2, a, 2) → J_1
  67. Circle(I_1, G_1) → e_2
  68. Circle(J_1, H_1) → f_2
  69. Intersect(f_2, i, 1) → K_1
  70. Intersect(e_2, j, 1) → L_1
  71. Circle(L_1, I_1) → g_2
  72. Circle(K_1, J_1) → h_2
  73. Line(I_1, L_1) → n_1
  74. Line(J_1, K_1) → a_2
  75. Intersect(k_1, c_2, 2) → M_1
  76. Intersect(j, i) → N_1
  77. Intersect(p_1, d_2) → O_1, P_1, ,
  78. Line(G_1, M_1) → b_2
  79. Line(H_1, P_1) → i_2
  80. Intersect(m, n_1) → Q_1
  81. Intersect(a_1, n_1) → R_1
  82. Intersect(m_1, n_1) → S_1
  83. Intersect(b_1, n_1) → T_1
  84. Intersect(n_1, i_2) → U_1
  85. Intersect(n_1, a_2) → V_1
  86. Intersect(a_2, b_2) → W_1
  87. Intersect(b_1, b_2) → Z_1
  88. Intersect(q_1, b_2, 1) → A_2
  89. Intersect(j_1, a_2) → B_2
  90. Intersect(l_1, a_2) → C_2
  91. Intersect(i_1, a_2) → D_2
  92. Intersect(l, a_2) → E_2
  93. Circle(R_1, Q_1) → k_2
  94. Circle(T_1, S_1) → p_2
  95. Circle(V_1, U_1) → q_2
  96. Circle(B_2, W_1) → r_2
  97. Circle(D_2, C_2) → s_2
  98. Intersect(e_2, e, 2) → F_2
  99. Intersect(f_2, a, 2) → G_2
  100. Circle(F_2, I_1) → t_2
  101. Circle(G_2, J_1) → c_3
  102. Intersect(t_2, e, 2) → H_2
  103. Intersect(c_3, a, 2) → I_2
  104. OrthogonalLine(H_2, e) → j_2
  105. OrthogonalLine(F_2, e) → l_2
  106. OrthogonalLine(I_2, a) → m_2
  107. OrthogonalLine(G_2, a) → n_2
  108. Intersect(a_1, l_2) → J_2
  109. Intersect(b_1, l_2) → K_2
  110. Intersect(a_2, l_2) → L_2
  111. Intersect(n_1, n_2) → M_2
  112. Intersect(j_1, n_2) → N_2
  113. Intersect(i_1, n_2) → O_2
  114. Intersect(h_2, c_3, 2) → P_2
  115. Intersect(j, j_2) → Q_2
  116. Intersect(a_1, j_2) → R_2
  117. Intersect(b_1, j_2) → S_2
  118. Intersect(a_2, j_2) → T_2
  119. Intersect(j_2, m_2) → U_2
  120. Intersect(i, m_2) → V_2
  121. Intersect(i_1, m_2) → W_2
  122. Intersect(j_1, m_2) → Z_2
  123. Intersect(n_1, m_2) → A_3
  124. Circle(Q_2, H_2) → d_3
  125. Circle(R_2, J_2) → e_3
  126. Circle(S_2, K_2) → f_3
  127. Circle(T_2, L_2) → g_3
  128. Intersect(j_2, n_2) → B_3
  129. Circle(U_2, B_3) → h_3
  130. Circle(A_3, M_2) → k_3
  131. Circle(Z_2, N_2) → p_3
  132. Circle(W_2, O_2) → q_3
  133. Circle(V_2, P_2) → r_3
  134. Circle(Q_2, H_2) → s_3
  135. Circle(R_2, J_2) → t_3
  136. Circle(S_2, K_2) → c_4
  137. Circle(T_2, L_2) → d_4
  138. Circle(U_2, B_3) → e_4
  139. Circle(A_3, M_2) → f_4
  140. Circle(V_1, W_1) → g_4
  141. Circle(T_1, U_1) → h_4
  142. Circle(R_1, S_1) → k_4
  143. Circle(L_1, Q_1) → p_4
  144. Circle(S, M_1) → q_4
  145. Circle(A_1, A_2) → r_4
  146. Circle(D_1, Z_1) → s_4
  147. Circle(B_2, N_2) → t_4
  148. Circle(Z_2, N_2) → c_5
  149. Circle(W_2, O_2) → d_5
  150. Circle(V_2, P_2) → e_5
  151. Circle(K_1, E_2) → f_5
  152. Circle(D_2, C_2) → g_5
  153. Circle(C_1, F_1) → h_5
  154. Circle(T, P_1) → k_5
  155. Circle(P, V) → p_5
  156. Circle(B_1, F_1) → q_5
  157. Circle(R, U) → r_5
  158. Circle(G, E) → s_5

AI 绘图提示语参考

画一个正方形，内部画一个圆，圆与正方形边相切。在正方形内部，通过圆与坐标轴的交点构造一个四边形，并画出该四边形。接着，以正方形中心为圆心画一个稍大的圆，再以圆与坐标轴的交点为圆心画几个小圆，形成装饰图案。最后，连接一些关键点形成额外的线条，使图形更复杂美观。
以上提示语为根据原始绘图命令整理而来，仅供参考。