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根矩形

根矩形
几何画板及绘图内容加载中，请稍等……
2019-04-21 16:19
多边形向量几何作图
这个范例演示了根矩形的构造过程。根矩形是一种特殊的矩形，其对角线长度是边长的平方根。本例涉及的核心数学概念包括矩形、向量和几何作图。通过使用GeoGebra命令如Point、Segment、Polygon等，可以直观地展示根矩形的性质。适合初中及以上学生学习几何作图和相关概念。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → D
  4. Point(yAxis) → E
  5. Segment(O, P) → n
  6. Point(xAxis) → C
  7. Point(xAxis) → G
  8. Polygon(C, G, 4) → poly1, f, g, h, i, H, I
  9. Segment(C, H) → j
  10. Line(C, G) → k
  11. Circle(C, H) → c
  12. Intersect(c, k, 2) → J
  13. OrthogonalLine(J, k) → l
  14. Line(H, k) → m
  15. Intersect(l, m) → A_1
  16. Polygon(G, H, A_1, J) → q1, g_1, h_1, a_1, j_1
  17. Circle(C, A_1) → d
  18. Intersect(d, k, 2) → B_1
  19. Line(B_1, l) → p
  20. Intersect(m, p) → C_1
  21. Polygon(J, B_1, C_1, A_1) → q2, j_2, b_1, c_1, q
  22. Circle(C, C_1) → e
  23. Intersect(e, k, 2) → D_1
  24. Line(D_1, p) → r
  25. Intersect(m, r) → E_1
  26. Polygon(B_1, D_1, E_1, C_1) → q3, s, d_1, e_1, t
  27. Circle(C, E_1) → f_1
  28. Intersect(f_1, k, 2) → F_1
  29. Line(F_1, r) → a
  30. Intersect(m, a) → G_1
  31. Polygon(D_1, F_1, G_1, E_1) → q4, b, i_1, k_1, l_1
  32. Circle(C, G_1) → p_1
  33. Intersect(p_1, k, 2) → H_1
  34. Line(H_1, a) → m_1
  35. Intersect(m, m_1) → I_1
  36. Polygon(F_1, H_1, I_1, G_1) → q5, n_1, q_1, r_1, s_1
  37. Circle(C, I_1) → t_1
  38. Intersect(t_1, k, 2) → J_1
  39. Line(J_1, m_1) → f_2
  40. Intersect(m, f_2) → K_1
  41. Polygon(H_1, J_1, K_1, I_1) → q6, g_2, h_2, i_2, k_2
  42. Circle(C, K_1) → c_2
  43. Intersect(c_2, k, 2) → L_1
  44. Line(L_1, f_2) → l_2
  45. Intersect(m, l_2) → M_1
  46. Polygon(J_1, L_1, M_1, K_1) → q7, m_2, n_2, p_2, q_2
  47. Circle(C, M_1) → d_2
  48. Intersect(d_2, k, 2) → N_1
  49. Line(N_1, l_2) → r_2
  50. Intersect(m, r_2) → O_1
  51. Polygon(L_1, N_1, O_1, M_1) → q8, s_2, t_2, o_1, a_2
  52. CircleArc(C, J, H) → e_2
  53. CircleArc(C, B_1, A_1) → c_3
  54. CircleArc(C, D_1, C_1) → d_3
  55. CircleArc(C, F_1, E_1) → e_3
  56. CircleArc(C, J_1, I_1) → f_3
  57. CircleArc(C, H_1, G_1) → g_3
  58. CircleArc(C, L_1, K_1) → h_3
  59. CircleArc(C, N_1, M_1) → k_3
  60. Segment(G, I) → b_2
  61. Circle(C, G) → p_3
  62. Circle(G, C) → q_3
  63. Intersect(q_3, b_2, 1) → P_1
  64. Intersect(p_3, j, 1) → Q_1
  65. Line(P_1, Q_1) → i_3
  66. Intersect(i_3, i) → R_1
  67. Intersect(i_3, g) → S_1
  68. Distance(P_1, Q_1) → distanceP1Q1
  69. Intersect(p_3, i_3, 1) → T_1
  70. Segment(C, S_1) → j_3
  71. Segment(G, R_1) → l_3
  72. Intersect(p_3, j_3, 1) → U_1
  73. Intersect(q_3, l_3, 1) → V_1
  74. Line(V_1, U_1) → m_3
  75. Intersect(m_3, i) → W_1
  76. Intersect(m_3, g) → Z_1
  77. Distance(V_1, U_1) → distanceV1U1
  78. Segment(C, Z_1) → n_3
  79. Segment(G, W_1) → r_3
  80. Intersect(q_3, r_3, 1) → A_2
  81. Intersect(p_3, n_3, 1) → B_2
  82. Line(A_2, B_2) → s_3
  83. Intersect(s_3, i) → C_2
  84. Intersect(s_3, g) → D_2
  85. Distance(A_2, B_2) → distanceA2B2
  86. Segment(P_1, T_1) → t_3
  87. Segment(V_1, U_1) → a_3
  88. Segment(A_2, B_2) → b_3
  89. Segment(R_1, S_1) → f_4
  90. Segment(W_1, Z_1) → g_4
  91. Segment(C_2, D_2) → h_4
  92. Segment(C, D_2) → i_4
  93. Segment(G, C_2) → j_4
  94. Intersect(q_3, j_4, 1) → E_2
  95. Intersect(p_3, i_4, 1) → F_2
  96. Distance(E_2, F_2) → distanceE2F2
  97. Intersect(p_3, i_4, 1) → G_2
  98. Segment(C, Z_1) → k_4
  99. Polygon(C, G, 4) → poly2, l_4, m_4, n_4, p_4, H_2, I_2
  100. Line(E_2, G_2) → q_4
  101. Intersect(q_4, p_4) → J_2
  102. Intersect(q_4, g_1) → K_2
  103. Segment(C, K_2) → r_4
  104. Segment(G, J_2) → s_4
  105. Segment(E_2, G_2) → t_4
  106. Segment(J_2, K_2) → a_4
  107. Intersect(p_3, r_4, 1) → L_2
  108. Intersect(q_3, s_4, 1) → M_2
  109. Segment(M_2, L_2) → b_4
  110. Line(M_2, L_2) → c_4
  111. Intersect(c_4, p_4) → N_2
  112. Intersect(c_4, g_1) → O_2
  113. Segment(C, O_2) → d_4
  114. Segment(G, N_2) → e_4
  115. Segment(N_2, O_2) → f_5
  116. Intersect(q_3, e_4, 1) → P_2
  117. Intersect(p_3, d_4, 1) → Q_2
  118. Segment(P_2, Q_2) → g_5
  119. Line(P_2, Q_2) → h_5
  120. Intersect(h_5, p_4) → R_2
  121. Intersect(h_5, g_1) → S_2
  122. Segment(C, S_2) → i_5
  123. Segment(G, R_2) → j_5
  124. Intersect(q_3, j_5, 1) → T_2
  125. Intersect(p_3, i_5, 1) → U_2
  126. Segment(T_2, U_2) → k_5
  127. Segment(R_2, S_2) → l_5
  128. Line(T_2, U_2) → m_5
  129. Intersect(m_5, p_4) → V_2
  130. Intersect(m_5, g_1) → W_2
  131. Segment(C, W_2) → n_5
  132. Segment(G, V_2) → p_5
  133. Segment(V_2, W_2) → q_5
  134. Intersect(q_3, p_5, 1) → Z_2
  135. Intersect(p_3, n_5, 1) → A_3
  136. Segment(Z_2, A_3) → r_5
  137. Line(Z_2, A_3) → s_5
  138. Intersect(s_5, p_4) → B_3
  139. Intersect(s_5, g_1) → C_3
  140. Segment(B_3, C_3) → t_5
  141. Segment(C, C_3) → a_5
  142. Segment(G, B_3) → b_5
  143. Intersect(q_3, b_5, 1) → D_3
  144. Intersect(p_3, a_5, 1) → E_3
  145. Segment(D_3, E_3) → c_5
  146. Line(D_3, E_3) → d_5
  147. Intersect(d_5, p_4) → F_3
  148. Intersect(d_5, g_1) → G_3
  149. Segment(C, G_3) → e_5
  150. Segment(G, F_3) → f_6
  151. Intersect(q_3, f_6, 1) → H_3
  152. Intersect(p_3, e_5, 1) → I_3
  153. Segment(H_3, I_3) → g_6
  154. Line(H_3, I_3) → h_6
  155. Intersect(h_6, p_4) → J_3
  156. Intersect(h_6, g_1) → K_3

AI 绘图提示语参考

绘制一个根矩形，首先在x轴上创建点A、B、D和C，在y轴上创建点E。然后以C为圆心，H为半径画圆，与直线CH相交得到点J。通过J作CH的垂线，与先前的直线相交得到点A1。接着以A1为圆心，C为半径画圆，与直线CH相交得到点B1，以此类推，最终形成一个根矩形的网格。
以上提示语为根据原始绘图命令整理而来，仅供参考。