Venn图 - 互动

Venn图 - 互动
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2020-07-22 00:35
该范例演示了互动Venn图,涉及集合论的核心概念。通过使用Polygon, Intersect, Circle, Point等GeoGebra命令,可以构建两个或三个集合的交集、并集和补集。适合初中及以上学生学习集合的基本运算。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Intersect(a, d) → E
  3. Intersect(a, b) → F
  4. Intersect(b, c) → G
  5. Intersect(c, d) → H
  6. Polygon(E, F, G, H) → q2, e, f, g, h
  7. Circle(I, 2) → k
  8. Circle(J, 2) → p
  9. Circle(K, 1.97) → q
  10. Circle(L, 1.97) → r
  11. Circle(M, 1.97) → s
  12. Circle(N, 1.97) → t
  13. Intersect(k, p, 2) → O
  14. Point(p) → P
  15. Point(p) → Q
  16. Point(p) → R
  17. Point(p) → S
  18. Point(p) → T
  19. Point(p) → U
  20. Point(p) → V
  21. Point(p) → W
  22. Intersect(k, p, 1) → Z
  23. Point(k) → A_1
  24. Point(k) → B_1
  25. Point(k) → C_1
  26. Point(k) → D_1
  27. Point(k) → E_1
  28. Point(k) → F_1
  29. Point(k) → G_1
  30. Point(k) → H_1
  31. Point(k) → I_1
  32. Point(k) → J_1
  33. Point(k) → K_1
  34. Point(k) → L_1
  35. Point(k) → M_1
  36. Point(k) → N_1
  37. Point(k) → O_1
  38. Point(k) → P_1
  39. Point(k) → Q_1
  40. Point(k) → R_1
  41. Point(k) → S_1
  42. Point(k) → T_1
  43. Point(k) → U_1
  44. Point(k) → V_1
  45. Point(k) → W_1
  46. Point(k) → Z_1
  47. Point(k) → A_2
  48. Point(k) → B_2
  49. Point(k) → C_2
  50. Point(k) → D_2
  51. Point(k) → E_2
  52. Polygon(O, P, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, Q, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, R, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, S, T, U, V, W, Z) → poly1, o, z_1, a_1, b_1, c_1, d_1, e_1, f_1, g_1, h_1, i_1, p_1, j_1, k_1, l_1, m_1, n_1, o_1, f_2, g_2, h_2, i_2, q_1, j_2, u_1, v_1, w_1, k_2, a_2, b_2, c_2, d_2, e_2, r_1, s_1, t_1, u, v, w
  53. Intersect(k, p, 2) → F_2
  54. Point(p) → G_2
  55. Point(p) → H_2
  56. Point(p) → I_2
  57. Point(p) → J_2
  58. Point(p) → K_2
  59. Point(p) → L_2
  60. Point(p) → M_2
  61. Point(p) → N_2
  62. Point(p) → O_2
  63. Point(p) → P_2
  64. Point(p) → Q_2
  65. Point(p) → R_2
  66. Point(p) → S_2
  67. Point(p) → T_2
  68. Point(p) → U_2
  69. Point(p) → V_2
  70. Point(p) → W_2
  71. Point(p) → Z_2
  72. Point(p) → A_3
  73. Point(p) → B_3
  74. Point(p) → C_3
  75. Point(p) → D_3
  76. Point(p) → E_3
  77. Point(p) → F_3
  78. Intersect(k, p, 1) → G_3
  79. Point(k) → H_3
  80. Point(k) → I_3
  81. Point(k) → J_3
  82. Point(k) → K_3
  83. Point(k) → L_3
  84. Point(k) → M_3
  85. Point(k) → N_3
  86. Point(k) → O_3
  87. Point(k) → P_3
  88. Point(k) → Q_3
  89. Polygon(F_2, G_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, H_2, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3, I_2, L_3, M_3, N_3, O_3, P_3, Q_3, J_2, K_2, L_2, M_2, N_2, O_2) → poly2, m_2, o_2, h_3, i_3, j_3, k_3, l_3, u_2, v_2, w_2, z_2, n_2, a_3, b_3, c_3, d_3, e_3, m_3, n_3, p_3, q_3, r_3, p_2, s_3, t_3, f_4, g_4, o_3, h_4, i_4, q_2, r_2, s_2, t_2, f_3, g_3
  90. Polygon(O, Q_3, H_3, Z, W, V, U, T, S, R, Q, P, P_3, O_3, N_3, M_3, L_3, K_3, J_3, I_3) → poly3, o_4, s_4, t_4, z_3, w_3, v_3, u_4, t_5, s_5, r_5, q_5, j_4, p_5, k_4, l_4, m_4, n_4, p_4, q_4, r_4
  91. Polygon(O, Q_3, H_3, Z, W, V, U, T, S, R, Q, P, P_3, O_3, N_3, M_3, L_3, K_3, J_3, I_3) → poly4, o_5, j_5, k_5, z_4, w_4, v_4, u_5, t_6, s_6, r_6, q_6, b_4, p_6, c_4, d_4, e_4, f_5, g_5, h_5, i_5
  92. Circle(R_3, 2) → c_5
  93. Circle(S_3, 1.97) → d_5
  94. Intersect(k, c_5, 2) → T_3
  95. Point(c_5) → U_3
  96. Point(c_5) → V_3
  97. Point(c_5) → W_3
  98. Point(c_5) → Z_3
  99. Intersect(k, c_5, 1) → A_4
  100. Point(k) → B_4
  101. Point(k) → C_4
  102. Point(k) → D_4
  103. Point(k) → E_4
  104. Point(k) → F_4
  105. Point(k) → G_4
  106. Point(k) → H_4
  107. Point(k) → I_4
  108. Point(k) → J_4
  109. Point(k) → K_4
  110. Point(k) → L_4
  111. Point(k) → M_4
  112. Point(k) → N_4
  113. Point(k) → O_4
  114. Point(k) → P_4
  115. Polygon(T_3, U_3, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, V_3, P_4, W_3, Z_3, A_4, B_4, C_4, D_4, E_4) → poly5, l_5, k_6, l_6, m_6, n_6, a_6, b_6, c_6, d_6, e_6, f_7, m_5, g_7, h_7, n_5, e_5, f_6, g_6, h_6, i_6, j_6
  116. Intersect(k, c_5, 2) → Q_4
  117. Point(k) → R_4
  118. Point(k) → S_4
  119. Point(k) → T_4
  120. Point(k) → U_4
  121. Point(k) → V_4
  122. Point(k) → W_4
  123. Intersect(k, c_5, 1) → Z_4
  124. Point(c_5) → A_5
  125. Point(c_5) → B_5
  126. Point(c_5) → C_5
  127. Point(c_5) → D_5
  128. Point(c_5) → E_5
  129. Point(c_5) → F_5
  130. Point(c_5) → G_5
  131. Point(c_5) → H_5
  132. Point(c_5) → I_5
  133. Point(c_5) → J_5
  134. Point(c_5) → K_5
  135. Point(c_5) → L_5
  136. Point(c_5) → M_5
  137. Point(c_5) → N_5
  138. Point(c_5) → O_5
  139. Point(c_5) → P_5
  140. Point(c_5) → Q_5
  141. Polygon(Q_4, R_4, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, K_5, L_5, S_4, M_5, N_5, O_5, P_5, Q_5, T_4, U_4, V_4, W_4, Z_4, A_5, B_5) → poly6, i_7, s_7, t_7, a_7, b_7, c_7, d_7, e_7, f_8, g_8, h_8, j_7, i_8, j_8, k_8, l_8, m_8, n_8, k_7, l_7, m_7, n_7, p_7, q_7, r_7
  142. Intersect(p, c_5, 2) → R_5
  143. Point(p) → S_5
  144. Point(p) → T_5
  145. Point(p) → U_5
  146. Point(p) → V_5
  147. Point(p) → W_5
  148. Point(p) → Z_5
  149. Point(p) → A_6
  150. Point(p) → B_6
  151. Point(p) → C_6
  152. Intersect(p, c_5, 1) → D_6
  153. Point(c_5) → E_6
  154. Point(c_5) → G_6
  155. Point(c_5) → H_6
  156. Point(c_5) → I_6
  157. Point(c_5) → J_6
  158. Point(c_5) → K_6
  159. Point(c_5) → L_6
  160. Point(c_5) → M_6
  161. Point(c_5) → N_6
  162. Point(c_5) → O_6
  163. Point(c_5) → P_6
  164. Point(c_5) → Q_6
  165. Point(c_5) → R_6
  166. Point(c_5) → S_6
  167. Point(c_5) → T_6
  168. Point(c_5) → U_6
  169. Point(c_5) → V_6
  170. Point(c_5) → W_6
  171. Point(c_5) → Z_6
  172. Point(c_5) → A_7
  173. Point(c_5) → B_7
  174. Polygon(R_5, S_5, D_6, E_6, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, T_5, N_6, O_6, P_6, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, U_5, Z_6, A_7, B_7, V_5, W_5, Z_5, A_6, B_6, C_6) → poly7, p_8, d_8, e_8, f_9, g_9, h_9, i_9, j_9, k_9, l_9, m_9, q_8, n_9, p_9, o_6, q_9, r_9, s_9, t_9, a_9, u_6, v_6, r_8, w_6, z_6, b_9, c_9, s_8, t_8, a_8, z_5, b_8, c_8
  175. Intersect(p, c_5, 2) → C_7
  176. Point(c_5) → D_7
  177. Point(c_5) → E_7
  178. Point(c_5) → F_7
  179. Point(c_5) → G_7
  180. Point(c_5) → H_7
  181. Point(c_5) → I_7
  182. Intersect(p, c_5, 1) → J_7
  183. Point(p) → K_7
  184. Point(p) → L_7
  185. Point(p) → M_7
  186. Point(p) → N_7
  187. Point(p) → O_7
  188. Point(p) → P_7
  189. Point(p) → Q_7
  190. Point(p) → R_7
  191. Point(p) → S_7
  192. Point(p) → T_7
  193. Point(p) → U_7
  194. Point(p) → V_7
  195. Point(p) → W_7
  196. Point(p) → Z_7
  197. Point(p) → A_8
  198. Intersect(k, p, 1) → B_8
  199. Point(p) → C_8
  200. Point(p) → D_8
  201. Point(p) → E_8
  202. Polygon(C_7, D_7, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7, E_7, W_7, Z_7, A_8, B_8, C_8, D_8, E_8, F_7, G_7, H_7, I_7, J_7, K_7, L_7) → poly8, d_9, m_{10}, n_{10}, p_{10}, q_{10}, r_{10}, s_{10}, t_{10}, a_{10}, b_{10}, u_7, e_9, v_7, w_7, z_7, c_{10}, d_{10}, e_{10}, f_{11}, g_{11}, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}
  203. Intersect(p, c_5, 2) → F_8
  204. Point(p) → G_8
  205. Point(p) → H_8
  206. Point(p) → I_8
  207. Intersect(k, p, 1) → J_8
  208. Point(k) → K_8
  209. Point(k) → L_8
  210. Point(k) → M_8
  211. Point(k) → N_8
  212. Point(k) → O_8
  213. Point(k) → P_8
  214. Point(k) → Q_8
  215. Point(k) → R_8
  216. Point(k) → S_8
  217. Point(k) → T_8
  218. Point(k) → U_8
  219. Point(k) → V_8
  220. Point(k) → W_8
  221. Point(k) → Z_8
  222. Point(k) → A_9
  223. Intersect(k, c_5, 2) → B_9
  224. Point(c_5) → C_9
  225. Point(c_5) → D_9
  226. Point(c_5) → E_9
  227. Point(c_5) → F_9
  228. Polygon(F_8, G_8, P_8, Q_8, R_8, S_8, T_8, U_8, V_8, W_8, Z_8, A_9, H_8, B_9, C_9, D_9, E_9, F_9, I_8, J_8, K_8, L_8, M_8, N_8, O_8) → poly9, h_{11}, r_{11}, s_{11}, t_{11}, a_{11}, b_{11}, c_{11}, u_8, v_8, w_8, z_8, i_{11}, d_{11}, e_{11}, f_{12}, g_{12}, h_{12}, i_{12}, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}
  229. Intersect(p, c_5, 1) → G_9
  230. Point(c_5) → H_9
  231. Point(c_5) → I_9
  232. Point(c_5) → J_9
  233. Point(c_5) → K_9
  234. Intersect(k, c_5, 1) → L_9
  235. Point(k) → M_9
  236. Point(k) → N_9
  237. Point(k) → O_9
  238. Intersect(k, p, 1) → P_9
  239. Point(p) → Q_9
  240. Point(p) → R_9
  241. Point(p) → S_9
  242. Point(p) → T_9
  243. Point(p) → U_9
  244. Point(p) → V_9
  245. Point(p) → W_9
  246. Point(p) → Z_9
  247. Point(p) → A_{10}
  248. Point(p) → B_{10}
  249. Point(p) → C_{10}
  250. Point(p) → D_{10}
  251. Polygon(G_9, H_9, Q_9, R_9, S_9, T_9, U_9, V_9, W_9, Z_9, A_{10}, B_{10}, I_9, C_{10}, D_{10}, J_9, K_9, L_9, M_9, N_9, O_9, P_9) → poly10, j_{12}, t_{12}, a_{12}, b_{12}, c_{12}, d_{12}, u_9, v_9, w_9, z_9, e_{12}, k_{12}, f_{13}, g_{13}, h_{13}, l_{12}, m_{12}, n_{12}, p_{12}, q_{12}, r_{12}, s_{12}
  252. Intersect(p, c_5, 1) → E_{10}
  253. Point(p) → F_{10}
  254. Point(p) → G_{10}
  255. Point(p) → H_{10}
  256. Point(p) → I_{10}
  257. Point(p) → J_{10}
  258. Intersect(k, p, 2) → K_{10}
  259. Point(k) → L_{10}
  260. Point(k) → M_{10}
  261. Point(k) → N_{10}
  262. Point(k) → O_{10}
  263. Point(k) → P_{10}
  264. Intersect(k, c_5, 2) → Q_{10}
  265. Point(c_5) → R_{10}
  266. Point(c_5) → S_{10}
  267. Point(c_5) → T_{10}
  268. Point(c_5) → U_{10}
  269. Point(c_5) → W_{10}
  270. Point(c_5) → Z_{10}
  271. Point(c_5) → A_{11}
  272. Point(c_5) → B_{11}
  273. Point(c_5) → C_{11}
  274. Point(c_5) → D_{11}
  275. Point(c_5) → E_{11}
  276. Point(c_5) → F_{11}
  277. Point(c_5) → G_{11}
  278. Point(c_5) → H_{11}
  279. Point(c_5) → I_{11}
  280. Point(c_5) → J_{11}
  281. Point(c_5) → K_{11}
  282. Polygon(E_{10}, F_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}, G_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, H_{10}, K_{11}, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, N_{10}) → poly11, i_{13}, s_{13}, t_{13}, a_{13}, b_{13}, c_{13}, d_{13}, e_{13}, u_{10}, v_{10}, w_{10}, j_{13}, z_{10}, f_{14}, g_{14}, h_{14}, i_{14}, j_{14}, k_{14}, l_{14}, m_{14}, n_{14}, k_{13}, p_{14}, q_{14}, l_{13}, m_{13}, n_{13}, p_{13}, q_{13}, r_{13}
  283. Intersect(k, c_5, 2) → L_{11}
  284. Point(c_5) → M_{11}
  285. Point(c_5) → N_{11}
  286. Point(c_5) → O_{11}
  287. Point(c_5) → P_{11}
  288. Intersect(k, c_5, 1) → Q_{11}
  289. Point(k) → R_{11}
  290. Intersect(k, p, 2) → S_{11}
  291. Point(k) → T_{11}
  292. Point(k) → U_{11}
  293. Point(k) → V_{11}
  294. Point(k) → W_{11}
  295. Polygon(L_{11}, M_{11}, V_{11}, W_{11}, N_{11}, O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}, U_{11}) → poly12, r_{14}, u_{11}, v_{11}, w_{11}, s_{14}, t_{14}, a_{14}, b_{14}, c_{14}, d_{14}, e_{14}, f_{15}
  296. Intersect(p, c_5, 2) → Z_{11}
  297. Point(p) → A_{12}
  298. Point(p) → B_{12}
  299. Point(p) → C_{12}
  300. Point(p) → D_{12}
  301. Point(p) → E_{12}
  302. Point(p) → F_{12}
  303. Intersect(p, c_5, 1) → G_{12}
  304. Point(c_5) → H_{12}
  305. Point(c_5) → I_{12}
  306. Point(c_5) → J_{12}
  307. Point(c_5) → K_{12}
  308. Point(c_5) → L_{12}
  309. Point(c_5) → M_{12}
  310. Point(c_5) → N_{12}
  311. Polygon(Z_{11}, A_{12}, J_{12}, K_{12}, L_{12}, M_{12}, N_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}) → poly13, z_{11}, p_{15}, q_{15}, r_{15}, s_{15}, t_{15}, a_{15}, g_{15}, h_{15}, i_{15}, j_{15}, k_{15}, l_{15}, m_{15}, n_{15}
  312. Intersect(p, c_5, 2) → O_{12}
  313. Point(c_5) → P_{12}
  314. Point(c_5) → Q_{12}
  315. Intersect(k, c_5, 1) → R_{12}
  316. Point(k) → S_{12}
  317. Point(k) → T_{12}
  318. Point(k) → U_{12}
  319. Intersect(k, p, 2) → V_{12}
  320. Point(p) → W_{12}
  321. Point(p) → Z_{12}
  322. Point(p) → A_{13}
  323. Point(p) → B_{13}
  324. Polygon(O_{12}, P_{12}, A_{13}, B_{13}, Q_{12}, R_{12}, S_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}) → poly14, b_{15}, z_{12}, i_{16}, j_{16}, c_{15}, d_{15}, e_{15}, f_{16}, g_{16}, h_{16}, v_{12}, w_{12}
  325. Circle(C_{13}, 1.98) → c_{16}