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集合演示

集合演示
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2017-08-07 01:21
变换几何作图
①本范例通过动态演示集合的交集、并集等操作，直观展示集合运算的几何意义；②涉及核心数学概念包括集合论、相似变换、全等、垂心及逻辑推理；③作图要点运用了多边形(Polygon)、圆(Circle)、交点(Intersect)、圆弧(CircleArc)等GeoGebra命令；④适合高中数学教学，用于帮助学生理解抽象的集合运算和几何变换。

GeoGebra 命令及参数

  1. Polygon(A_1, B_1, C, D) → Back, a_2, b_2, c_2, d_2
  2. Polygon(E, F, G, H) → Backblue, e_3, f_3, g_3, h_3
  3. Polygon(I, J, K, L) → OutlneBox, i, j, k, l
  4. Circle(M, N) → A'
  5. Circle(O, P) → B'
  6. Circle(Q, R) → A
  7. Circle(S, T) → B
  8. Circle(U, V) → OutlineA
  9. Circle(W, Z) → OutlineB
  10. Circle(Q_1, R_1) → A_2
  11. Circle(S_1, T_1) → B_2
  12. Polygon(E_1, F_1, G_1, H_1) → Backblue_1, e_1, f_1, g_1, h_1
  13. Circle(M_1, N_1) → A'_1
  14. Circle(O_1, P_1) → B'_1
  15. Circle(C_1, D_1) → p
  16. Circle(I_1, J_1) → q
  17. Intersect(p, q, 2) → K_1
  18. Intersect(p, q, 1) → L_1
  19. CircleArc(C_1, K_1, L_1) → Intersect1
  20. CircleArc(I_1, L_1, K_1) → Intersect2
  21. Circle(C_2, D_2) → p_1
  22. Circle(I_2, J_2) → q_1
  23. Intersect(p_1, q_1, 2) → K_2
  24. Intersect(p_1, q_1, 1) → L_2
  25. CircleArc(C_2, K_2, L_2) → Intersect1_1
  26. CircleArc(I_2, L_2, K_2) → Intersect2_1
  27. Polygon(A_3, B_3, C_3, D_3) → Back_1, a_1, b_1, c_1, d_1
  28. Polygon(E_2, F_2, G_2, H_2) → Backblue_2, e_2, f_2, g_2, h_2
  29. Circle(S_3, T_3) → B_4
  30. Circle(Q_3, R_3) → A_4
  31. Circle(C_4, D_4) → p_3
  32. Circle(I_3, J_3) → q_2
  33. Intersect(p_3, q_2, 2) → K_3
  34. Intersect(p_3, q_2, 1) → L_3
  35. CircleArc(C_4, K_3, L_3) → Intersect1_2
  36. CircleArc(I_3, L_3, K_3) → Intersect2_2
  37. Circle(C_5, D_5) → p_4
  38. Circle(I_4, J_4) → q_3
  39. Intersect(p_4, q_3, 2) → K_4
  40. Intersect(p_4, q_3, 1) → L_4
  41. CircleArc(C_5, K_4, L_4) → Intersect1_3
  42. CircleArc(I_4, L_4, K_4) → Intersect2_3
  43. Circle(C_6, D_6) → p_5
  44. Circle(I_5, J_5) → q_4
  45. Intersect(p_5, q_4, 2) → K_5
  46. Intersect(p_5, q_4, 1) → L_5
  47. CircleArc(C_6, K_5, L_5) → Intersect1_4
  48. CircleArc(I_5, L_5, K_5) → Intersect2_4
  49. Circle(C_7, D_7) → p_6
  50. Circle(I_6, J_6) → q_5
  51. Intersect(p_6, q_5, 2) → K_6
  52. Intersect(p_6, q_5, 1) → L_6
  53. CircleArc(C_7, K_6, L_6) → Intersect1_5
  54. CircleArc(I_6, L_6, K_6) → Intersect2_5
  55. Circle(Q_4, R_4) → A_5
  56. Circle(S_4, T_4) → B_5
  57. Circle(M_3, N_3) → A'_2
  58. Polygon(A_6, B_6, C_{13}, D_{13}) → Back_2, a_3, b_3, c_3, d_3
  59. Polygon(E_3, F_3, G_3, H_3) → Backblue_3, e_4, f_4, g_4, h_4
  60. Circle(O_3, P_3) → B'_2
  61. Polygon(A_8, B_8, C_{15}, D_{15}) → Back_4, a_5, b_5, c_5, d_5
  62. Polygon(A_9, B_9, C_{16}, D_{16}) → Back_3, a_4, b_4, c_4, d_4
  63. Polygon(E_4, F_4, G_4, H_4) → Backblue_4, e_5, f_5, g_5, h_5
  64. Circle(C_{18}, D_{18}) → p_7
  65. Circle(I_7, J_7) → q_6
  66. Intersect(p_7, q_6, 2) → K_7
  67. Intersect(p_7, q_6, 1) → L_7
  68. CircleArc(C_{18}, K_7, L_7) → Intersect1_6
  69. CircleArc(I_7, L_7, K_7) → Intersect2_6
  70. Circle(C_{19}, D_{19}) → p_8
  71. Circle(I_8, J_8) → q_7
  72. Intersect(p_8, q_7, 2) → K_8
  73. Intersect(p_8, q_7, 1) → L_8
  74. CircleArc(C_{19}, K_8, L_8) → Intersect1_7
  75. CircleArc(I_8, L_8, K_8) → Intersect2_7
  76. Polygon(A_{11}, B_{11}, C_{20}, D_{20}) → Back_5, a_6, b_6, c_6, d_6
  77. Polygon(E_6, F_6, G_6, H_6) → Backblue_5, e_6, f_6, g_6, h_6
  78. Circle(C_{24}, D_{24}) → p_9
  79. Circle(I_9, J_9) → q_8
  80. Intersect(p_9, q_8, 2) → K_9
  81. Intersect(p_9, q_8, 1) → L_9
  82. Circle(C_{25}, D_{25}) → p_{10}
  83. Circle(I_{10}, J_{10}) → q_9
  84. Intersect(p_{10}, q_9, 2) → K_{10}
  85. Intersect(p_{10}, q_9, 1) → L_{10}
  86. CircleArc(C_{25}, K_{10}, L_{10}) → Intersect1_8
  87. CircleArc(I_{10}, L_{10}, K_{10}) → LeftWIntersection
  88. Intersect(OutlineA, OutlineB, 2) → V_2
  89. Intersect(OutlineA, OutlineB, 1) → W_2
  90. CircleArc(U_2, V_2, W_2) → RightWIntersection
  91. Circle(M_5, N_5) → A'_3
  92. Circle(Q_8, R_8) → A_{15}
  93. Circle(M_8, N_8) → A'_4
  94. Circle(O_4, P_4) → B'_3
  95. Circle(C_{34}, D_{34}) → p_{11}
  96. Circle(I_{11}, J_{11}) → q_{10}
  97. Intersect(p_{11}, q_{10}, 2) → K_{11}
  98. Intersect(p_{11}, q_{10}, 1) → L_{11}
  99. CircleArc(C_{34}, K_{11}, L_{11}) → Intersect1_9
  100. Polygon(A_{16}, B_{15}, C_{42}, D_{42}) → Back_6, a_7, b_7, c_7, d_7
  101. Circle(O_5, P_5) → B'_4
  102. Circle(S_9, T_9) → B_{20}
  103. Circle(O_7, P_7) → B'_5
  104. Circle(O_{10}, P_{10}) → B'_6
  105. Circle(O_{13}, P_{13}) → B'_7
  106. Circle(S_{18}, T_{18}) → B_{21}
  107. Circle(M_{12}, N_{12}) → A'_6
  108. Circle(M_{13}, N_{13}) → A'_5
  109. Circle(Q_{14}, R_{14}) → A_{21}
  110. Circle(M_{19}, N_{19}) → A'_7
  111. Circle(O_{16}, P_{16}) → B'_8
  112. Circle(C_{63}, D_{63}) → p_{12}
  113. Circle(I_{51}, J_{51}) → q_{11}
  114. Intersect(p_{12}, q_{11}, 2) → K_{12}
  115. Intersect(p_{12}, q_{11}, 1) → L_{12}
  116. CircleArc(C_{63}, K_{12}, L_{12}) → Intersect1_{10}
  117. CircleArc(I_{51}, L_{12}, K_{12}) → LeftWIntersection_2
  118. Circle(M_{26}, N_{26}) → A'_9
  119. Circle(M_{25}, N_{25}) → A'_8
  120. Circle(O_{20}, P_{20}) → B'_9
  121. Polygon(E_8, F_8, G_8, H_8) → Backblue_6, e_7, f_7, g_7, h_7
  122. Circle(O_{25}, P_{25}) → B'_{10}
  123. Circle(M_{37}, N_{37}) → A'_{10}
  124. Circle(O_{35}, P_{35}) → B'_{11}
  125. Polygon(A_{22}, B_{22}, C_{103}, D_{103}) → Back_7, a_8, b_8, c_8, d_8
  126. Polygon(E_9, F_9, G_9, H_9) → Backblue_7, e_8, f_8, g_8, h_8
  127. Circle(M_{51}, N_{51}) → A'_{12}
  128. Circle(O_{51}, P_{51}) → B'_{13}
  129. Circle(M_{52}, N_{52}) → A'_{11}
  130. Circle(O_{52}, P_{52}) → B'_{12}
  131. Circle(C_{109}, D_{109}) → p_{13}
  132. Circle(I_{107}, J_{107}) → q_{12}
  133. Intersect(p_{13}, q_{12}, 2) → K_{13}
  134. Intersect(p_{13}, q_{12}, 1) → L_{13}
  135. CircleArc(C_{109}, K_{13}, L_{13}) → Intersect1_{11}
  136. CircleArc(I_{107}, L_{13}, K_{13}) → LeftWIntersection_1
  137. Circle(M_{65}, N_{65}) → A'_{15}
  138. Circle(M_{66}, N_{66}) → A'_{14}
  139. Circle(M_{67}, N_{67}) → A'_{13}
  140. Circle(Q_{41}, R_{41}) → A_{28}
  141. Circle(S_{48}, T_{48}) → B_{28}
  142. Circle(O_{73}, P_{73}) → B'_{14}
  143. Circle(M_{92}, N_{92}) → A'_{16}
  144. Circle(O_{83}, P_{83}) → B'_{15}
  145. Circle(C_{157}, D_{157}) → p_{14}
  146. Circle(I_{147}, J_{147}) → q_{13}
  147. Intersect(p_{14}, q_{13}, 2) → K_{14}
  148. Intersect(p_{14}, q_{13}, 1) → L_{14}
  149. CircleArc(C_{157}, K_{14}, L_{14}) → Intersect1_{12}
  150. CircleArc(I_{147}, L_{14}, K_{14}) → LeftWIntersection_3
  151. Circle(U_{61}, V_{25}) → OutlineA_1
  152. Circle(W_{32}, Z_{38}) → OutlineB_1
  153. Intersect(OutlineA_1, OutlineB_1, 2) → V_{31}
  154. Intersect(OutlineA_1, OutlineB_1, 1) → W_{38}
  155. CircleArc(U_{62}, V_{31}, W_{38}) → RightWIntersection_1
  156. Circle(M_{103}, N_{103}) → A'_{17}
  157. Circle(O_{93}, P_{93}) → B'_{16}
  158. Circle(U_{63}, V_{34}) → OutlineA_2
  159. Circle(W_{41}, Z_{39}) → OutlineB_2
  160. Intersect(OutlineA_2, OutlineB_2, 2) → V_{35}
  161. Intersect(OutlineA_2, OutlineB_2, 1) → W_{42}
  162. CircleArc(U_{64}, V_{35}, W_{42}) → RightWIntersection_2
  163. Circle(M_{115}, N_{115}) → A'_{19}
  164. Circle(O_{104}, P_{104}) → B'_{18}
  165. Circle(M_{116}, N_{116}) → A'_{18}
  166. Circle(O_{105}, P_{105}) → B'_{17}
  167. Circle(U_{71}, V_{39}) → OutlineA_3
  168. Circle(W_{46}, Z_{43}) → OutlineB_3
  169. Intersect(OutlineA_3, OutlineB_3, 2) → V_{40}
  170. Intersect(OutlineA_3, OutlineB_3, 1) → W_{47}
  171. CircleArc(U_{72}, V_{40}, W_{47}) → RightWIntersection_3
  172. Polygon(E_{11}, F_{11}, G_{11}, H_{11}) → poly1, e_{11}, f_{11}, g_{11}, h_{11}
  173. Polygon(E_{12}, F_{12}, G_{12}, H_{12}) → poly2, e_{12}, f_{12}, g_{12}, h_{12}
  174. Polygon(G_{13}, H_{13}, E_{14}, F_{14}) → poly3, g_{13}, h_{13}, e_{14}, f_{14}
  175. Polygon(G_{15}, H_{15}, K_{15}, L_{15}) → poly4, g_{15}, h_{15}, k_{15}, l_{15}

AI 绘图提示语参考

画两个不同颜色的多边形，再画三个圆，分别与多边形相交，用圆弧连接交点，展示集合的交集和并集，体现几何变换中的相似性和全等性，适合高中数学教学，帮助学生理解抽象的集合运算和几何变换。
以上提示语为根据原始绘图命令整理而来，仅供参考。