几何作图示例:8/2

几何作图示例:8/2
几何画板及绘图内容加载中,请稍等……
2020-08-18 00:23
该示例演示了如何通过几何作图构造特定的多边形。核心数学概念包括多边形、角、中点和镜像。使用了Intersect、ConstructionStep、Circle、Line、Mirror、Polygon、Segment、Sequence、Midpoint等GeoGebra命令。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. ConstructionStep() → stap
  3. Circle(A, B) → c
  4. Intersect(c, xAxis, 1) → D
  5. Line(D, B) → j_2
  6. Intersect(c, yAxis, 2) → C
  7. Intersect(c, f, 2) → E
  8. Mirror(E, yAxis) → E'
  9. Polygon(E, E', 4) → veelhoek1, g, h, i, j, F, G
  10. Polygon(B, C, 4) → veelhoek2, k, l, m, n, H, I
  11. Intersect(g, l) → J
  12. Intersect(i, m) → K
  13. Intersect(g, k) → L
  14. Intersect(i, n) → M
  15. Intersect(j, n) → N
  16. Intersect(j, k) → O
  17. Intersect(h, l) → P
  18. Intersect(h, m) → Q
  19. Segment(J, N) → p
  20. Segment(Q, L) → q
  21. Segment(P, O) → r
  22. Segment(J, K) → s
  23. Segment(L, M) → t
  24. Segment(Q, N) → a
  25. Segment(P, M) → b
  26. Segment(K, O) → d
  27. Intersect(r, s) → R
  28. Intersect(q, r) → S
  29. Intersect(p, q) → T
  30. Polygon(J, R, S, T) → vierhoek1, j_1, r_1, s_1, t_1
  31. Sequence(Polygon[Rotate[J, (nn * (-(45°)))], Rotate[R, (nn * (-(45°)))], Rotate[S, (nn * (-(45°)))], Rotate[T, (nn * (-(45°)))]], nn, -1, 2) → l1
  32. Polygon(P, R, 4) → veelhoek3, e, f_1, g_1, h_1, U, V
  33. Polygon(E, L, 4) → veelhoek4, i_1, k_1, l_1, m_1, W, Z
  34. Polygon(L, C, 4) → veelhoek5, n_1, p_1, q_1, a_1, A_1, B_1
  35. Polygon(B, O, 4) → veelhoek6, b_1, c_1, d_1, e_1, C_1, D_1
  36. Polygon(P, D, 4) → veelhoek7, f_2, g_2, h_2, i_2, E_1, F_1
  37. Line(E, B) → k_2
  38. Mirror(O, k_2) → O'
  39. Line(D, E') → l_2
  40. Mirror(P, l_2) → P'
  41. Line(E', C) → m_2
  42. Mirror(J, m_2) → J'
  43. Mirror(J', yAxis) → J''
  44. Polygon(D, P, E', P') → vierhoek2, d_2, p_2, e', p'
  45. Polygon(E', J, C, J') → vierhoek3, n_2, j_3, c_2, j'
  46. Polygon(C, L, E, J'') → vierhoek4, c_3, l_3, e_2, j''
  47. Polygon(E, O, B, O') → vierhoek5, e_3, o, b_2, o'
  48. Polygon(O', B, 4) → veelhoek9, a_2, f_3, g_3, h_3, I_1, J_1
  49. Polygon(D, P', 4) → veelhoek8, q_2, r_2, s_2, t_2, G_1, H_1
  50. Polygon(J', C, 4) → veelhoek10, i_3, k_3, m_3, n_3, K_1, L_1
  51. Polygon(C, J'', 4) → veelhoek11, p_3, q_3, r_3, s_3, M_1, N_1
  52. Polygon(J'', E, 4) → veelhoek12, t_3, a_3, b_3, d_3, O_1, P_1
  53. Polygon(E, O', 4) → veelhoek13, f_4, g_4, h_4, i_4, Q_1, R_1
  54. Polygon(P', E', 4) → veelhoek14, j_4, k_4, l_4, m_4, S_1, T_1
  55. Polygon(E', J', 4) → veelhoek15, n_4, p_4, q_4, r_4, U_1, V_1
  56. Line(U_1, L_1) → s_4
  57. Mirror(J', s_4) → J''_1
  58. Polygon(J', L_1, J''_1, U_1) → vierhoek6, t_4, a_4, j''_1, u_1
  59. Mirror(J''_1, yAxis) → W_1
  60. Polygon(J'', P_1, W_1, M_1) → vierhoek7, b_4, c_4, w_1, d_4
  61. Line(Q_1, J_1) → e_4
  62. Mirror(O', e_4) → O''
  63. Polygon(O', J_1, O'', Q_1) → vierhoek8, f_5, g_5, o'', h_5
  64. Mirror(O'', yAxis) → O'''
  65. Polygon(P', T_1, O''', G_1) → vierhoek9, i_5, j_5, o''', k_5
  66. Line(J''_1, K_1) → l_5
  67. Mirror(L_1, l_5) → Z_1
  68. Polygon(K_1, Z_1, J''_1, L_1) → vierhoek10, m_5, z_1, n_5, p_5
  69. Mirror(Z_1, yAxis) → A_2
  70. Polygon(K_1, M_1, W_1, A_2) → vierhoek11, q_5, r_5, s_5, t_5
  71. Line(S_1, J''_1) → a_5
  72. Mirror(U_1, a_5) → B_2
  73. Polygon(S_1, U_1, J''_1, B_2) → vierhoek12, b_5, c_5, d_5, e_5
  74. Mirror(B_2, yAxis) → C_2
  75. Polygon(O_1, C_2, W_1, P_1) → vierhoek13, o_1, f_6, g_6, h_6
  76. Line(T_1, B_2) → i_6
  77. Line(H_1, O''') → s_6
  78. Mirror(G_1, s_6) → F_2
  79. Polygon(H_1, G_1, O''', F_2) → vierhoek16, t_6, a_6, b_6, c_6
  80. Mirror(F_2, yAxis) → G_2
  81. Polygon(I_1, G_2, O'', J_1) → vierhoek17, d_6, e_6, f_7, g_7
  82. Line(O''', S_1) → j_6
  83. Mirror(T_1, j_6) → D_2
  84. Polygon(O''', T_1, S_1, D_2) → vierhoek14, k_6, l_6, m_6, n_6
  85. Mirror(P', O''') → P''
  86. Mirror(S_1, O''') → E_2
  87. Mirror(D_2, O''') → H_2
  88. Mirror(T_1, O''') → I_2
  89. Mirror(F_2, O''') → J_2
  90. Mirror(G_1, O''') → K_2
  91. Mirror(H_1, O''') → L_2
  92. Mirror(H_1, j_5) → M_2
  93. Polygon(O''', D_2, M_2, J_2) → vierhoek15, p_6, q_6, r_6, h_7
  94. Polygon(O''', J_2, L_2, K_2) → vierhoek18, i_7, j_7, k_7, l_7
  95. Polygon(O''', K_2, P'', I_2) → vierhoek19, m_7, n_7, p'', p_7
  96. Polygon(O''', I_2, E_2, H_2) → vierhoek20, q_7, r_7, s_7, t_7
  97. Mirror(M_2, O''') → N_2
  98. Polygon(O''', H_2, N_2, F_2) → vierhoek21, a_7, b_7, c_7, d_7
  99. Mirror(D_2, yAxis) → O_2
  100. Polygon(O'', O_2, O_1, Q_1) → vierhoek22, e_7, o_2, f_8, g_8
  101. Mirror(M_2, yAxis) → P_2
  102. Mirror(J_2, yAxis) → Q_2
  103. Polygon(O'', Q_2, P_2, O_2) → vierhoek23, h_8, i_8, j_8, k_8
  104. Mirror(P'', yAxis) → P'''
  105. Mirror(K_2, yAxis) → R_2
  106. Mirror(L_2, yAxis) → S_2
  107. Polygon(O'', R_2, S_2, Q_2) → vierhoek24, l_8, m_8, n_8, p_8
  108. Mirror(I_2, yAxis) → T_2
  109. Polygon(O'', T_2, P''', R_2) → vierhoek25, q_8, r_8, p''', s_8
  110. Mirror(E_2, yAxis) → U_2
  111. Mirror(H_2, yAxis) → V_2
  112. Polygon(O'', V_2, U_2, T_2) → vierhoek26, t_8, v_2, u_2, a_8
  113. Mirror(N_2, yAxis) → W_2
  114. Polygon(O'', G_2, W_2, V_2) → vierhoek27, b_8, c_8, w_2, d_8
  115. Polygon(N_2, H_2, 4) → veelhoek16, e_8, f_9, g_9, h_9, Z_2, A_3
  116. Polygon(D_2, S_1, 4) → veelhoek17, i_9, j_9, k_9, l_9, B_3, C_3
  117. Polygon(O_1, O_2, 4) → veelhoek18, m_9, n_9, p_9, q_9, D_3, E_3
  118. Polygon(V_2, W_2, 4) → veelhoek19, r_9, s_9, t_9, a_9, F_3, G_3
  119. Polygon(E_2, I_2, 4) → veelhoek20, b_9, c_9, d_9, e_9, H_3, I_3
  120. Polygon(P'', K_2, 4) → veelhoek21, f_{10}, g_{10}, h_{10}, i_{10}, J_3, K_3
  121. Polygon(J_2, M_2, 4) → veelhoek22, j_{10}, k_{10}, l_{10}, m_{10}, L_3, M_3
  122. Polygon(Q_2, S_2, 4) → veelhoek23, n_{10}, p_{10}, q_{10}, r_{10}, N_3, O_3
  123. Polygon(R_2, P''', 4) → veelhoek24, s_{10}, t_{10}, a_{10}, b_{10}, P_3, Q_3
  124. Polygon(T_2, U_2, 4) → veelhoek25, c_{10}, d_{10}, e_{10}, f_{11}, R_3, S_3
  125. Polygon(K_1, A_2, 4) → veelhoek26, g_{11}, h_{11}, i_{11}, j_{11}, T_3, U_3
  126. Mirror(B_2, J''_1) → V_3
  127. Polygon(J''_1, Z_1, T_3, V_3) → vierhoek28, k_{11}, l_{11}, m_{11}, v_3
  128. Mirror(Z_1, J''_1) → W_3
  129. Polygon(J''_1, W_3, M_2, B_2) → vierhoek29, n_{11}, w_3, p_{11}, q_{11}
  130. Mirror(L_1, J''_1) → Z_3
  131. Mirror(U_1, J''_1) → A_4
  132. Mirror(S_1, J''_1) → B_4
  133. Polygon(J''_1, V_3, B_4, A_4) → vierhoek30, r_{11}, s_{11}, t_{11}, a_{11}
  134. Mirror(J', J''_1) → J''_2
  135. Polygon(J''_1, A_4, J''_2, Z_3) → vierhoek31, b_{11}, c_{11}, j''_2, z_3
  136. Mirror(K_1, J''_1) → C_4
  137. Polygon(J''_1, Z_3, C_4, W_3) → vierhoek32, d_{11}, e_{11}, f_{12}, g_{12}
  138. Mirror(B_4, yAxis) → D_4
  139. Mirror(J''_2, yAxis) → E_4
  140. Mirror(A_4, yAxis) → F_4
  141. Mirror(V_3, yAxis) → G_4
  142. Polygon(W_1, G_4, T_3, A_2) → vierhoek33, h_{12}, i_{12}, j_{12}, k_{12}
  143. Mirror(C_4, yAxis) → H_4
  144. Mirror(W_3, yAxis) → I_4
  145. Polygon(W_1, C_2, P_2, I_4) → vierhoek34, l_{12}, m_{12}, n_{12}, p_{12}
  146. Polygon(W_1, F_4, D_4, G_4) → vierhoek35, q_{12}, r_{12}, s_{12}, t_{12}
  147. Mirror(Z_3, yAxis) → J_4
  148. Polygon(W_1, J_4, E_4, F_4) → vierhoek36, a_{12}, b_{12}, c_{12}, d_{12}
  149. Polygon(I_4, H_4, J_4, W_1) → vierhoek37, e_{12}, f_{13}, g_{13}, h_{13}
  150. Midpoint(B_4, D_4) → K_4
  151. Polygon(V_3, T_3, K_4, B_4) → vierhoek38, i_{13}, j_{13}, k_{13}, l_{13}
  152. Segment(C_4, L_3) → m_{13}
  153. Segment(H_4, N_3) → n_{13}
  154. Segment(K_4, D_4) → p_{13}
  155. Polygon(C_4, Z_3, 4) → veelhoek27, q_{13}, r_{13}, s_{13}, t_{13}, L_4, M_4
  156. Polygon(J_4, H_4, 4) → veelhoek28, a_{13}, b_{13}, c_{13}, d_{13}, N_4, O_4
  157. Polygon(J''_2, A_4, 4) → veelhoek29, e_{13}, f_{14}, g_{14}, h_{14}, P_4, Q_4
  158. Polygon(D_4, F_4, 4) → veelhoek30, i_{14}, j_{14}, k_{14}, l_{14}, R_4, S_4

AI 绘图提示语参考

画一个由多个多边形和四边形组成的复杂几何图形,包含中心点和坐标轴交点。首先绘制一个圆,然后通过圆与坐标轴的交点构造线段和角度。利用镜像和旋转操作创建多个对称的多边形和四边形,最后用线段连接关键点形成复杂的几何图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。