GeoGebra 五格拼图

GeoGebra 五格拼图
几何画板及绘图内容加载中,请稍等……
2014-04-16 13:01
①本范例演示使用五格拼图进行几何拼接与挑战选择;②涉及核心数学概念包括几何变换、多边形拼接、空间想象;③作图要点:运用了 Circle, Point, Line, OrthogonalLine, Intersect, Vector, Translate, Segment, Polygon, Mirror 等GeoGebra命令与对象;④适合初中及以上学生用于几何学习与空间能力培养。

GeoGebra 命令及参数

  1. Circle(D, a) → c
  2. Circle(D, (4 * a)) → k
  3. Point(k) → M
  4. Line(D, M) → d
  5. OrthogonalLine(D, d) → e
  6. Intersect(c, e, 2) → E
  7. Intersect(c, e, 1) → F
  8. Intersect(c, d, 1) → G
  9. Intersect(c, d, 2) → H
  10. Line(E, d) → f
  11. Line(F, d) → g
  12. Line(H, e) → h
  13. Line(G, e) → i
  14. Intersect(f, i) → I
  15. Intersect(g, i) → J
  16. Intersect(f, h) → K
  17. Intersect(g, h) → L
  18. Vector(J, L) → w
  19. Vector(J, I) → z
  20. Translate(K, w) → K'_1
  21. Translate(L, w) → L'
  22. Translate(K'_1, w) → K''_1
  23. Translate(L', w) → L''
  24. Translate(I, z) → I'_1
  25. Translate(K, z) → K'
  26. Vector(K, I) → j
  27. Translate(I'_1, j) → I''_1
  28. Translate(I, j) → I'
  29. Point(d) → N
  30. Circle(N, flipcircle) → p
  31. Intersect(p, d, 1) → O
  32. Intersect(p, d, 2) → P
  33. Segment(O, P) → l
  34. Point(l) → Q
  35. Segment(O, Q) → m
  36. Polygon(I''_1, I', I, J, L'', K''_1, K, K') → poly1, i'', i', i_1, j_1, l'', k'', k_1, k'
  37. Mirror(I''_1, l) → I'''
  38. Mirror(I'_1, l) → S
  39. Mirror(K', l) → K''
  40. Mirror(I', l) → I''
  41. Polygon(I''', K'', L, L'', K''_1, I, J, I'') → poly2, i''', k''_1, l_1, l''_1, k''_2, i_2, j_2, i''_1
  42. Circle(T, a) → r
  43. Circle(T, (6 * a)) → s
  44. Point(s) → U
  45. Line(T, U) → t
  46. OrthogonalLine(T, t) → a_1
  47. Intersect(r, a_1, 2) → V
  48. Intersect(r, t, 1) → W
  49. Intersect(r, a_1, 1) → Z
  50. Intersect(r, t, 2) → A_1
  51. Line(V, t) → b_1
  52. Line(Z, t) → c_1
  53. Line(W, a_1) → d_1
  54. Line(A_1, a_1) → e_1
  55. Intersect(b_1, d_1) → B_1
  56. Intersect(c_1, d_1) → C_1
  57. Intersect(c_1, e_1) → D_1
  58. Intersect(b_1, e_1) → E_1
  59. Vector(C_1, D_1) → u
  60. Vector(C_1, B_1) → v
  61. Vector(E_1, D_1) → n
  62. Vector(E_1, B_1) → q
  63. Translate(D_1, Vector[(3 * u)]) → A
  64. Translate(E_1, Vector[(3 * u)]) → B
  65. Translate(B_1, v) → C
  66. Translate(E_1, v) → R
  67. Mirror(C, t) → C'
  68. Mirror(R, t) → R'
  69. Point(t) → F_1
  70. Point(t) → G_1
  71. Segment(F_1, G_1) → f_1
  72. Point(f_1) → H_1
  73. Segment(F_1, H_1) → g_1
  74. Polygon(C, C_1, A, B, E_1, R) → poly3, c_2, c_3, a_2, b_2, e_2, r_1
  75. Polygon(C', R', D_1, A, B, B_1) → poly4, c', r', d_2, a_3, b_3, b_4
  76. Circle(I_1, a) → h_1
  77. Circle(I_1, (4 * a)) → p_1
  78. Point(p_1) → J_1
  79. Line(I_1, J_1) → m_1
  80. OrthogonalLine(I_1, m_1) → n_1
  81. Intersect(h_1, n_1, 2) → K_1
  82. Intersect(h_1, m_1, 1) → L_1
  83. Intersect(h_1, n_1, 1) → M_1
  84. Intersect(h_1, m_1, 2) → N_1
  85. Line(K_1, m_1) → q_1
  86. Line(M_1, m_1) → s_1
  87. Line(L_1, n_1) → t_1
  88. Line(N_1, n_1) → f_2
  89. Intersect(q_1, t_1) → O_1
  90. Intersect(s_1, t_1) → P_1
  91. Intersect(s_1, f_2) → Q_1
  92. Intersect(q_1, f_2) → R_1
  93. Vector(P_1, Q_1) → u_1
  94. Vector(P_1, O_1) → v_1
  95. Translate(Q_1, Vector[(2 * u_1)]) → T_1
  96. Translate(R_1, u_1) → S_1
  97. Translate(T_1, Vector[(2 * v_1)]) → U_1
  98. Translate(S_1, v_1) → V_1
  99. Translate(P_1, Vector[(-1 * v_1)]) → W_1
  100. Translate(Q_1, Vector[(-1 * v_1)]) → Z_1
  101. Polygon(Z_1, Q_1, T_1, U_1, V_1, S_1, O_1, W_1) → poly5, z_1, q_2, t_2, u_2, v_2, s_2, o_1, w_1
  102. Mirror(W_1, m_1) → D_2
  103. Mirror(Z_1, m_1) → E_2
  104. Mirror(V_1, m_1) → F_2
  105. Mirror(U_1, m_1) → G_2
  106. Translate(T_1, v_1) → I_2
  107. Point(m_1) → A_2
  108. Point(m_1) → B_2
  109. Point(m_1) → C_2
  110. Segment(A_2, C_2) → g_2
  111. Point(g_2) → H_2
  112. Segment(H_2, A_2) → h_2
  113. Translate(F_2, v_1) → J_2
  114. Polygon(D_2, P_1, J_2, F_2, G_2, I_2, R_1, E_2) → poly6, d_3, p_2, j_3, f_3, g_3, i_3, r_2, e_3
  115. Circle(K_2, a) → k_2
  116. Circle(K_2, (4 * a)) → h_3
  117. Point(h_3) → L_2
  118. Line(K_2, L_2) → l_2
  119. OrthogonalLine(K_2, l_2) → m_2
  120. Intersect(k_2, m_2, 2) → M_2
  121. Intersect(k_2, l_2, 1) → N_2
  122. Intersect(k_2, m_2, 1) → O_2
  123. Intersect(k_2, l_2, 2) → P_2
  124. Line(M_2, l_2) → n_2
  125. Line(O_2, l_2) → k_3
  126. Line(N_2, m_2) → l_3
  127. Line(P_2, m_2) → m_3
  128. Intersect(n_2, l_3) → Q_2
  129. Intersect(k_3, l_3) → R_2
  130. Intersect(k_3, m_3) → S_2
  131. Intersect(n_2, m_3) → T_2
  132. Vector(R_2, S_2) → w_2
  133. Vector(R_2, Q_2) → z_2
  134. Translate(S_2, w_2) → U_2
  135. Translate(U_2, w_2) → V_2
  136. Translate(T_2, w_2) → W_2
  137. Translate(W_2, w_2) → Z_2
  138. Translate(T_2, z_2) → A_3
  139. Translate(W_2, z_2) → B_3
  140. Translate(U_2, Vector[(-1 * z_2)]) → C_3
  141. Translate(V_2, Vector[(-1 * z_2)]) → D_3
  142. Point(l_2) → E_3
  143. Point(l_2) → F_3
  144. Segment(E_3, F_3) → n_3
  145. Point(n_3) → G_3
  146. Segment(E_3, G_3) → p_3
  147. Polygon(R_2, U_2, C_3, D_3, Z_2, W_2, B_3, A_3, T_2, Q_2) → poly7, r_3, q_3, u_3, c_4, d_4, z_3, w_3, b_5, a_4, t_3
  148. Mirror(A_3, l_2) → H_3
  149. Mirror(D_3, l_2) → I_3
  150. Polygon(R_2, S_2, H_3, C_3, U_2, V_2, I_3, B_3, W_2, Q_2) → poly8, r_4, q_4, s_3, h_4, c_5, u_4, v_3, i_4, b_6, w_4
  151. Circle(J_3, a) → e_4
  152. Circle(J_3, (6 * a)) → f_4
  153. Point(f_4) → K_3
  154. Line(J_3, K_3) → g_4
  155. OrthogonalLine(J_3, g_4) → j_4
  156. Intersect(e_4, j_4, 2) → L_3
  157. Intersect(e_4, g_4, 1) → M_3
  158. Intersect(e_4, j_4, 1) → N_3
  159. Intersect(e_4, g_4, 2) → O_3
  160. Line(L_3, g_4) → k_4
  161. Line(N_3, g_4) → l_4
  162. Line(M_3, j_4) → m_4
  163. Line(O_3, j_4) → n_4
  164. Intersect(k_4, m_4) → P_3
  165. Intersect(l_4, m_4) → Q_3
  166. Intersect(l_4, n_4) → R_3
  167. Intersect(k_4, n_4) → S_3
  168. Vector(Q_3, R_3) → v_4
  169. Vector(Q_3, P_3) → z_4
  170. Translate(R_3, v_4) → T_3
  171. Translate(T_3, v_4) → U_3
  172. Translate(U_3, v_4) → V_3
  173. Translate(S_3, v_4) → W_3
  174. Translate(W_3, v_4) → Z_3
  175. Translate(Z_3, v_4) → A_4
  176. Translate(S_3, z_4) → B_4
  177. Translate(W_3, z_4) → C_4
  178. Mirror(B_4, g_4) → D_4
  179. Mirror(C_4, g_4) → E_4
  180. Point(g_4) → G_4
  181. Point(g_4) → H_4
  182. Segment(G_4, H_4) → p_4
  183. Point(p_4) → I_4
  184. Segment(G_4, I_4) → s_4
  185. Polygon(Q_3, V_3, A_4, W_3, C_4, B_4, S_3, P_3) → poly9, q_5, v_5, a_5, w_5, c_6, b_7, s_5, p_5
  186. Polygon(P_3, A_4, V_3, T_3, E_4, D_4, R_3, Q_3) → poly10, p_6, a_6, v_6, t_4, e_5, d_5, r_5, q_6
  187. Circle(J_4, a) → f_5
  188. Circle(J_4, (4 * a)) → g_5
  189. Point(g_5) → K_4
  190. Line(J_4, K_4) → h_5
  191. OrthogonalLine(J_4, h_5) → i_5
  192. Intersect(f_5, i_5, 2) → L_4
  193. Intersect(f_5, i_5, 1) → M_4
  194. Intersect(f_5, h_5, 1) → N_4
  195. Intersect(f_5, h_5, 2) → O_4
  196. Line(L_4, h_5) → j_5
  197. Line(M_4, h_5) → k_5
  198. Line(N_4, i_5) → l_5
  199. Line(O_4, i_5) → m_5
  200. Intersect(j_5, l_5) → P_4
  201. Intersect(k_5, l_5) → Q_4
  202. Intersect(k_5, m_5) → R_4
  203. Intersect(j_5, m_5) → S_4
  204. Vector(Q_4, P_4) → u_5
  205. Vector(Q_4, R_4) → z_5
  206. Translate(R_4, z_5) → T_4
  207. Translate(T_4, z_5) → U_4
  208. Translate(P_4, u_5) → V_4
  209. Translate(V_4, z_5) → W_4
  210. Translate(W_4, z_5) → Z_4
  211. Translate(T_4, u_5) → A_5
  212. Translate(U_4, u_5) → B_5
  213. Point(h_5) → C_5
  214. Point(h_5) → D_5
  215. Mirror(V_4, h_5) → E_5
  216. Mirror(W_4, h_5) → F_5
  217. Mirror(Z_4, h_5) → G_5
  218. Segment(C_5, D_5) → n_5
  219. Point(n_5) → H_5
  220. Segment(C_5, H_5) → t_5
  221. Polygon(V_4, Q_4, U_4, B_5, A_5, Z_4) → poly11, v_7, q_7, u_6, b_8, a_7, z_6
  222. Polygon(P_4, B_5, U_4, T_4, G_5, E_5) → poly12, p_7, b_9, u_7, t_6, g_6, e_6
  223. Circle(I_5, a) → d_6
  224. Circle(I_5, (8 * a)) → f_6
  225. Point(f_6) → J_5
  226. Line(I_5, J_5) → h_6
  227. OrthogonalLine(I_5, h_6) → i_6
  228. Intersect(d_6, i_6, 2) → K_5
  229. Intersect(d_6, h_6, 1) → L_5
  230. Intersect(d_6, i_6, 1) → M_5
  231. Intersect(d_6, h_6, 2) → N_5
  232. Line(K_5, h_6) → j_6
  233. Line(M_5, h_6) → k_6
  234. Line(L_5, i_6) → l_6
  235. Line(N_5, i_6) → m_6
  236. Intersect(j_6, l_6) → O_5
  237. Intersect(k_6, l_6) → P_5
  238. Intersect(k_6, m_6) → Q_5
  239. Intersect(j_6, m_6) → R_5
  240. Vector(P_5, Q_5) → w_6
  241. Translate(Q_5, Vector[(4 * w_6)]) → S_5
  242. Translate(R_5, Vector[(4 * w_6)]) → T_5
  243. Polygon(P_5, S_5, T_5, O_5) → poly13, p_8, s_6, t_7, o_5
  244. Circle(U_5, a) → r_6
  245. Circle(U_5, (4 * a)) → c_7
  246. Point(c_7) → V_5
  247. Line(U_5, V_5) → n_6
  248. OrthogonalLine(U_5, n_6) → d_7
  249. Intersect(r_6, d_7, 2) → W_5
  250. Intersect(r_6, d_7, 1) → Z_5
  251. Intersect(r_6, n_6, 1) → A_6
  252. Intersect(r_6, n_6, 2) → B_6
  253. Line(W_5, n_6) → e_7
  254. Line(Z_5, n_6) → f_7
  255. Line(A_6, d_7) → g_7
  256. Line(B_6, d_7) → h_7
  257. Intersect(e_7, g_7) → C_6
  258. Intersect(f_7, g_7) → D_6
  259. Intersect(f_7, h_7) → E_6
  260. Intersect(e_7, h_7) → F_6
  261. Vector(D_6, E_6) → w_7
  262. Vector(D_6, C_6) → z_7
  263. Vector(F_6, E_6) → i_7
  264. Translate(E_6, i_7) → G_6
  265. Translate(G_6, w_7) → H_6
  266. Translate(H_6, z_7) → I_6
  267. Translate(I_6, w_7) → J_6
  268. Translate(J_6, z_7) → K_6
  269. Translate(F_6, w_7) → L_6
  270. Translate(L_6, z_7) → M_6
  271. Translate(F_6, z_7) → N_6
  272. Polygon(D_6, E_6, F_6, C_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6) → poly14, d_8, n_7, f_8, c_8, e_8, g_8, h_8, i_8, j_7, k_7, l_7, m_7
  273. Circle(O_6, a) → r_7
  274. Circle(O_6, (4 * a)) → s_7
  275. Point(s_7) → P_6
  276. Line(O_6, P_6) → a_8
  277. OrthogonalLine(O_6, a_8) → j_8
  278. Intersect(r_7, j_8, 2) → Q_6
  279. Intersect(r_7, a_8, 1) → R_6
  280. Intersect(r_7, j_8, 1) → S_6
  281. Intersect(r_7, a_8, 2) → T_6
  282. Line(Q_6, a_8) → k_8
  283. Line(S_6, a_8) → l_8
  284. Line(R_6, j_8) → m_8
  285. Line(T_6, j_8) → n_8
  286. Intersect(k_8, m_8) → U_6
  287. Intersect(l_8, m_8) → V_6
  288. Intersect(l_8, n_8) → W_6
  289. Intersect(k_8, n_8) → Z_6
  290. Vector(V_6, W_6) → u_8
  291. Vector(V_6, U_6) → v_8
  292. Translate(W_6, Vector[(2 * u_8)]) → A_7
  293. Translate(Z_6, Vector[(2 * u_8)]) → B_7
  294. Translate(U_6, Vector[(2 * v_8)]) → C_7
  295. Translate(Z_6, Vector[(2 * v_8)]) → D_7
  296. Polygon(V_6, A_7, B_7, Z_6, D_7, C_7) → poly15, v_9, a_9, b_{10}, z_8, d_9, c_9
  297. Circle(E_7, a) → q_8
  298. Circle(E_7, (4 * a)) → r_8
  299. Point(r_8) → F_7
  300. Line(E_7, F_7) → s_8
  301. OrthogonalLine(E_7, s_8) → t_8
  302. Intersect(q_8, t_8, 2) → G_7
  303. Intersect(q_8, s_8, 1) → H_7
  304. Intersect(q_8, t_8, 1) → I_7
  305. Intersect(q_8, s_8, 2) → J_7
  306. Line(G_7, s_8) → e_9
  307. Line(I_7, s_8) → f_9
  308. Line(H_7, t_8) → g_9
  309. Line(J_7, t_8) → h_9
  310. Intersect(e_9, g_9) → K_7
  311. Intersect(f_9, g_9) → L_7
  312. Intersect(f_9, h_9) → M_7
  313. Intersect(e_9, h_9) → N_7
  314. Vector(L_7, M_7) → w_8
  315. Vector(L_7, K_7) → u_9
  316. Translate(M_7, Vector[(2 * w_8)]) → O_7
  317. Translate(N_7, Vector[(2 * w_8)]) → P_7
  318. Translate(N_7, w_8) → Q_7
  319. Translate(N_7, Vector[(2 * u_9)]) → R_7
  320. Translate(Q_7, Vector[(2 * u_9)]) → S_7
  321. Polygon(L_7, O_7, P_7, Q_7, S_7, R_7, N_7, K_7) → poly16, l_9, o_7, p_9, q_9, s_9, r_9, n_9, k_9
  322. Circle(T_7, a) → t_9
  323. Circle(T_7, (2 * a)) → c_{10}
  324. Point(c_{10}) → U_7
  325. Line(T_7, U_7) → i_9
  326. OrthogonalLine(T_7, i_9) → j_9
  327. Intersect(t_9, j_9, 2) → V_7
  328. Intersect(t_9, i_9, 1) → W_7
  329. Intersect(t_9, j_9, 1) → Z_7
  330. Intersect(t_9, i_9, 2) → A_8
  331. Line(V_7, i_9) → m_9
  332. Line(Z_7, i_9) → a_{10}
  333. Line(W_7, j_9) → d_{10}
  334. Line(A_8, j_9) → e_{10}
  335. Intersect(m_9, d_{10}) → B_8
  336. Intersect(a_{10}, d_{10}) → C_8
  337. Intersect(a_{10}, e_{10}) → D_8
  338. Intersect(m_9, e_{10}) → E_8
  339. Vector(C_8, D_8) → w_9
  340. Vector(C_8, B_8) → z_9
  341. Vector(E_8, D_8) → u_{10}
  342. Vector(E_8, B_8) → v_{10}
  343. Translate(D_8, w_9) → F_8
  344. Translate(F_8, z_9) → G_8
  345. Translate(G_8, z_9) → H_8
  346. Translate(E_8, z_9) → I_8
  347. Translate(B_8, z_9) → J_8
  348. Translate(J_8, v_{10}) → K_8
  349. Translate(C_8, v_{10}) → L_8
  350. Polygon(L_8, F_8, H_8, I_8, E_8, B_8, J_8, K_8) → poly17, l_{10}, f_{10}, h_{10}, i_{10}, e_{11}, b_{11}, j_{10}, k_{10}
  351. Circle(M_8, a) → g_{10}
  352. Circle(M_8, (2 * a)) → p_{10}
  353. Point(p_{10}) → N_8
  354. Line(M_8, N_8) → m_{10}
  355. OrthogonalLine(M_8, m_{10}) → n_{10}
  356. Intersect(g_{10}, n_{10}, 2) → O_8
  357. Intersect(g_{10}, m_{10}, 1) → P_8
  358. Intersect(g_{10}, n_{10}, 1) → Q_8
  359. Intersect(g_{10}, m_{10}, 2) → R_8
  360. Line(O_8, m_{10}) → q_{10}
  361. Line(Q_8, m_{10}) → r_{10}
  362. Line(P_8, n_{10}) → s_{10}
  363. Line(R_8, n_{10}) → t_{10}
  364. Intersect(q_{10}, s_{10}) → S_8
  365. Intersect(r_{10}, s_{10}) → T_8
  366. Intersect(r_{10}, t_{10}) → U_8
  367. Intersect(q_{10}, t_{10}) → V_8
  368. Vector(T_8, U_8) → w_{10}
  369. Vector(V_8, S_8) → z_{10}
  370. Vector(T_8, S_8) → u_{11}
  371. Vector(V_8, U_8) → v_{11}
  372. Translate(U_8, w_{10}) → W_8
  373. Translate(V_8, w_{10}) → Z_8
  374. Translate(V_8, u_{11}) → A_9
  375. Translate(S_8, u_{11}) → B_9
  376. Translate(S_8, z_{10}) → C_9
  377. Translate(C_9, u_{11}) → D_9
  378. Translate(D_9, u_{11}) → E_9
  379. Translate(B_9, u_{11}) → F_9
  380. Polygon(T_8, W_8, Z_8, V_8, A_9, B_9, F_9, E_9, C_9, S_8) → poly18, t_{11}, s_{11}, w_{11}, z_{11}, v_{12}, a_{11}, b_{12}, f_{11}, e_{12}, c_{11}
  381. Polygon(G_9, H_9, J_9, I_9) → poly19, g_{11}, h_{11}, j_{11}, i_{11}
  382. Polygon(G_9, L_9, K_9, M_9) → poly20, g_{12}, l_{11}, k_{11}, m_{11}

AI 绘图提示语参考

绘制一个由多个五边形组成的几何图形。首先画一个圆 c,然后画一个更大的圆 k,从中选取点 M。通过 M 画一条线 d,再画 d 的垂线 e,与圆 c 交于 E 和 F。接着画 d 和 e 的交点 G 和 H,以及 f、g、h、i 等线段和点,通过平移和镜像操作,最终形成两个五边形 poly1 和 poly2。
以上提示语为根据原始绘图命令整理而来,仅供参考。