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基础图形

基础图形
几何画板及绘图内容加载中，请稍等……
2020-04-30 16:44
向量解析几何几何作图
①本范例演示了基本几何图形的绘制与变换；②涉及的核心数学概念包括几何作图、变换、向量与坐标几何；③作图要点：使用了 Rotate（旋转）、Ray（射线）、Intersect（交点）、Segment（线段）、Mirror（镜像）、Point（点）、Polygon（多边形）、Midpoint（中点）、Vector（向量）、Line（直线）、CircleArc（圆弧）、Circle（圆）、Plane（平面）、Distance（距离）、OrthogonalLine（垂线）、Sequence（数列）等 GeoGebra 命令与对象；④适合初中及以上学生学习几何作图与空间想象能力。

GeoGebra 命令及参数

  1. Rotate(B_1, 45°, A_1) → C_1
  2. Rotate(C_1, (-(22.5°)), A_1) → J_1
  3. Ray(A_1, J_1) → l_2
  4. Intersect(vgl1, l_2) → N_1
  5. Segment(V, U) → g_2
  6. Rotate(V, 22.5°, Z) → V'
  7. Ray(Z, V') → f_2
  8. Mirror(V, f_2) → V'_1
  9. Intersect(g_2, f_2) → I_1
  10. Point(yAxis) → A
  11. Polygon(A, B, 4) → veelhoek1, f, g, h, i, C, D
  12. Point(yAxis) → E
  13. Rotate(F, (-(67.5°)), E) → F'
  14. Point(yAxis) → H
  15. Rotate(H, (-(22.5°)), G) → H'
  16. Ray(G, H') → j
  17. Ray(E, F') → k
  18. Intersect(j, k) → I
  19. Polygon(E, I, G, F) → vierhoek1, e, i_1, g_1, f_1
  20. Point(yAxis) → K
  21. Point(yAxis) → L
  22. Rotate(L, (-(22.5°)), M) → L'
  23. Rotate(L, 22.5°, K) → L'_1
  24. Ray(K, L'_1) → l
  25. Ray(M, L') → m
  26. Intersect(l, m) → N
  27. Polygon(K, L, M, N) → vierhoek2, k_1, l_1, m_1, n
  28. Point(yAxis) → O
  29. Intersect(xAxis, yAxis) → P
  30. Point(xAxis) → Q
  31. Polygon((1, 0), (1, 1), (0, 1)) → driehoek1, p, q, b_9
  32. Rotate(S, 45°, R) → S'
  33. Polygon(R, S, T, S') → vierhoek3, r, s, t, s'
  34. Midpoint(V, U) → W
  35. Rotate(W, (-(90°)), U) → W'
  36. Polygon(Z, V, I_1, V'_1) → vierhoek4, h_2, i_2, j_2, k_2
  37. Midpoint(D_1, C_1) → E_1
  38. Polygon(A_1, B_1, N_1, C_1) → vierhoek5, a_1, b_1, c_1, e_1
  39. Point(xAxis) → F_1
  40. Point(xAxis) → G_1
  41. Rotate(G_1, 45°, F_1) → H_1
  42. Polygon(F_1, G_1, H_1) → driehoek2, h_1, a, b
  43. Vector(A, D) → u
  44. Vector(A, B) → d
  45. Vector(D, C) → u_1
  46. Vector(B, C) → v_1
  47. Vector(I, E) → w_1
  48. Vector(I, G) → d_1
  49. Vector(E, F) → j_1
  50. Vector(G, F) → n_1
  51. Vector(L, K) → p_1
  52. Vector(L, M) → q_1
  53. Vector(M, N) → r_1
  54. Vector(K, N) → s_1
  55. Segment(O, Q) → t_1
  56. Vector(R, S') → w_2
  57. Vector(R, S) → a_2
  58. Vector(S, T) → b_2
  59. Vector(S', T) → c_2
  60. Vector(I_1, V) → v
  61. Vector(I_1, V'_1) → w
  62. Vector(V, Z) → d_2
  63. Vector(V'_1, Z) → e_2
  64. Line(K_1, L_1) → m_2
  65. Intersect(m_2, l_2) → M_1
  66. Line(A_1, B_1) → n_2
  67. Vector(A_1, C_1) → p_2
  68. Vector(A_1, B_1) → q_2
  69. Segment(C_1, N_1) → r_2
  70. Segment(N_1, B_1) → s_2
  71. Segment(H_1, G_1) → t_2
  72. Vector(H_1, F_1) → u_3
  73. Vector(G_1, F_1) → v_3
  74. Intersect(yAxis, xAxis) → O_1
  75. Point(xAxis) → P_1
  76. Point(zAxis) → Q_1
  77. Segment(O_1, Q_1) → verthoek00
  78. Segment(P_1, R_1) → verthoek0
  79. Segment(Q_1, R_1) → f_3
  80. CircleArc(U_1, W_1, T_1) → boog0
  81. Segment(S_1, T_1) → vertmidden0
  82. Segment(W_1, V_1) → vertklein0
  83. Segment(P_1, S_1) → onder0
  84. Segment(R_1, V_1) → boven0
  85. Line(U_1, V_1) → as
  86. Rotate(P_1, (-(90°)), as) → Z_1
  87. Rotate(S_1, (-(90°)), as) → A_2
  88. Segment(Z_1, A_2) → onder0'
  89. Rotate(R_1, (-(90°)), as) → B_2
  90. Rotate(V_1, (-(90°)), as) → C_2
  91. Segment(B_2, C_2) → boven0'
  92. Rotate(boog0, (-(90°)), as) → boog0'
  93. Rotate(S_1, (-(90°)), as) → D_2
  94. Rotate(T_1, (-(90°)), as) → E_2
  95. Segment(D_2, E_2) → vertmidden0'
  96. Segment(Q_1, B_2) → g_3
  97. Intersect(as, xOyPlane) → F_2
  98. Rotate(P_1, (-(90°)), as) → G_2
  99. Rotate(R_1, (-(90°)), as) → H_2
  100. Segment(G_2, H_2) → verthoek0'
  101. Polygon(P_1, F_2, Z_1, O_1) → vierhoek6, h_3, i_3, z_1, o_1
  102. Segment(K_2, P_1) → j_3
  103. Segment(Z_1, L_2) → k_3
  104. Segment(O_1, J_2) → l_3
  105. Segment(J_2, K_2) → m_3
  106. Segment(J_2, L_2) → n_3
  107. Segment(I_2, P_1) → p_3
  108. Segment(I_2, Z_1) → q_3
  109. Circle(P_1, 0.2, j_3) → c_3
  110. Plane(O_1, F_2, J_2) → diag
  111. Segment(K_2, M_2) → r_3
  112. Segment(M_2, L_2) → s_3
  113. Segment(M_2, I_2) → t_3
  114. CircleArc(P_2, Q_2, O_2) → d_3
  115. Segment(K_2, R_2) → a_3
  116. Segment(R_2, Q_2) → b_3
  117. Segment(O_2, N_2) → e_3
  118. Segment(P_1, N_2) → f_4
  119. Mirror(K_2, diag) → S_2
  120. Mirror(R_2, diag) → T_2
  121. Segment(S_2, T_2) → g_4
  122. Mirror(d_3, diag) → c_4
  123. Mirror(O_2, diag) → U_2
  124. Mirror(N_2, diag) → V_2
  125. Segment(U_2, V_2) → h_4
  126. Mirror(P_1, diag) → W_2
  127. Mirror(N_2, diag) → Z_2
  128. Segment(W_2, Z_2) → i_4
  129. Segment(C_3, P_1) → j_4
  130. Segment(A_3, O_1) → k_4
  131. Circle(P_1, 0.2, j_4) → d_4
  132. Segment(I_2, P_1) → l_4
  133. Intersect(l_4, d_4) → D_3, E_3
  134. Segment(Z_1, I_2) → m_4
  135. Distance(E_3, I_2) → o_2
  136. Distance(I_2, P_1) → o_3
  137. CircleArc(J_3, H_3, I_3) → e_4
  138. Segment(I_3, E_3) → n_4
  139. Segment(P_1, E_3) → p_4
  140. Segment(C_3, K_3) → q_4
  141. Segment(K_3, H_3) → r_4
  142. Segment(O_1, P_1) → s_4
  143. Mirror(C_3, diag) → M_3
  144. Mirror(K_3, diag) → N_3
  145. Segment(M_3, N_3) → t_4
  146. Mirror(e_4, diag) → c_5
  147. Mirror(I_3, diag) → O_3
  148. Mirror(E_3, diag) → P_3
  149. Segment(O_3, P_3) → a_4
  150. Mirror(C_3, diag) → Q_3
  151. Mirror(P_1, diag) → R_3
  152. Segment(Q_3, R_3) → b_4
  153. Mirror(P_1, diag) → S_3
  154. Mirror(E_3, diag) → T_3
  155. Segment(S_3, T_3) → f_5
  156. Mirror(O_1, diag) → U_3
  157. Mirror(P_1, diag) → V_3
  158. Segment(U_3, V_3) → g_5
  159. Segment(A_3, C_3) → h_5
  160. Mirror(A_3, diag) → W_3
  161. Mirror(C_3, diag) → Z_3
  162. Segment(W_3, Z_3) → i_5
  163. Segment(C_4, A_4) → k_5
  164. Segment(B_4, A_4) → q_5
  165. Mirror(D_4, diag) → H_4
  166. Mirror(O_1, diag) → I_4
  167. Mirror(E_4, diag) → J_4
  168. Mirror(D_4, diag) → K_4
  169. Segment(J_4, K_4) → s_5
  170. Mirror(C_4, diag) → L_4
  171. Mirror(A_4, diag) → M_4
  172. Segment(L_4, M_4) → t_5
  173. Mirror(A_4, diag) → N_4
  174. Mirror(G_4, diag) → O_4
  175. Segment(R_4, P_1) → j_5
  176. Segment(S_4, O_1) → f_6
  177. Polygon(O_1, P_1, T_4, P_4) → vierhoek7, g_6, h_6, i_6, j_6
  178. Circle(P_1, 0.2, j_5) → c_6
  179. Intersect(h_6, c_6) → U_4,
  180. CircleArc(W_4, Z_4, V_4) → d_6
  181. Segment(V_4, U_4) → k_6
  182. Segment(R_4, A_5) → l_6
  183. Segment(A_5, Z_4) → m_6
  184. Segment(U_4, P_1) → n_6
  185. Plane(O_1, T_4, S_4) → diag1
  186. Mirror(U_4, diag1) → B_5
  187. Mirror(P_1, diag1) → C_5
  188. Segment(B_5, C_5) → p_6
  189. Mirror(R_4, diag1) → D_5
  190. Mirror(P_1, diag1) → E_5
  191. Segment(D_5, E_5) → q_6
  192. Mirror(V_4, diag1) → F_5
  193. Mirror(U_4, diag1) → G_5
  194. Segment(F_5, G_5) → r_6
  195. Mirror(d_6, diag1) → e_6
  196. Mirror(R_4, diag1) → H_5
  197. Mirror(A_5, diag1) → I_5
  198. Segment(H_5, I_5) → s_6
  199. Segment(S_4, R_4) → t_6
  200. Segment(S_4, H_5) → a_6
  201. Segment(L_5, J_5) → b_6
  202. OrthogonalLine(L_5, b_6, xOyPlane) → f_7
  203. Intersect(f_7, yAxis) → M_5
  204. Segment(K_5, M_5) → g_7
  205. Segment(M_5, L_5) → h_7
  206. Segment(K_5, J_5) → i_7
  207. Segment(O_5, L_5) → j_7
  208. Segment(O_5, P_5) → k_7
  209. Segment(N_5, O_5) → l_7
  210. Segment(N_5, M_5) → m_7
  211. Circle(L_5, 0.2, j_7) → c_7
  212. Intersect(b_6, c_7) → Q_5,
  213. CircleArc(S_5, T_5, R_5) → d_7
  214. Segment(P_5, T_5) → n_7
  215. Segment(R_5, Q_5) → p_7
  216. Segment(L_5, Q_5) → q_7
  217. Plane(M_5, J_5, N_5) → diag2
  218. Mirror(R_5, diag2) → U_5
  219. Mirror(Q_5, diag2) → V_5
  220. Segment(U_5, V_5) → r_7
  221. Mirror(P_5, diag2) → W_5
  222. Mirror(T_5, diag2) → Z_5
  223. Segment(W_5, Z_5) → s_7
  224. Mirror(L_5, diag2) → A_6
  225. Mirror(Q_5, diag2) → B_6
  226. Segment(A_6, B_6) → t_7
  227. Mirror(d_7, diag2) → e_7
  228. Mirror(O_5, diag2) → C_6
  229. Mirror(L_5, diag2) → D_6
  230. Segment(C_6, D_6) → a_7
  231. Mirror(N_5, diag2) → E_6
  232. Mirror(O_5, diag2) → F_6
  233. Segment(E_6, F_6) → b_7
  234. Mirror(O_5, diag2) → G_6
  235. Mirror(P_5, diag2) → H_6
  236. Segment(G_6, H_6) → f_8
  237. Rotate(P_1, 45°, zAxis) → I_6
  238. Segment(J_6, P_1) → g_8
  239. Segment(I_6, J_6) → h_8
  240. Segment(I_6, O_1) → i_8
  241. Segment(O_1, P_1) → j_8
  242. Segment(M_6, P_1) → l_8
  243. Segment(K_6, Q_6) → n_8
  244. Segment(Q_6, L_6) → p_8
  245. Mirror(Q_6, diag1) → R_6
  246. Mirror(L_6, diag1) → S_6
  247. Segment(R_6, S_6) → r_8
  248. Mirror(K_6, diag1) → T_6
  249. Mirror(Q_6, diag1) → U_6
  250. Segment(T_6, U_6) → s_8
  251. Mirror(N_6, diag1) → V_6
  252. Mirror(M_6, diag1) → W_6
  253. Mirror(M_6, diag1) → Z_6
  254. Mirror(P_1, diag1) → A_7
  255. Mirror(Q_6, diag1) → B_7
  256. Mirror(P_1, diag1) → C_7
  257. Segment(T_6, K_6) → e_8
  258. Rotate(A_4, 45°, zAxis) → D_7
  259. Rotate(G_4, 45°, zAxis) → E_7
  260. Rotate(D_4, 45°, zAxis) → F_7
  261. Rotate(O_1, 45°, zAxis) → G_7
  262. Rotate(E_4, 45°, zAxis) → H_7
  263. Rotate(D_4, 45°, zAxis) → I_7
  264. Rotate(C_4, 45°, zAxis) → J_7
  265. Rotate(A_4, 45°, zAxis) → K_7
  266. Segment(J_7, K_7) → j_9
  267. Segment(A_4, D_5) → k_9
  268. Segment(G_7, P_1) → m_9
  269. Segment(G_7, L_7) → n_9
  270. Segment(L_7, P_1) → p_9
  271. Segment(P_1, Z_1) → r_9
  272. Segment(O_1, P_1) → s_9
  273. Segment(O_1, Z_1) → t_9
  274. Vector(LO, LB) → w_3
  275. Vector(LO, RO) → u_4
  276. Vector(LB, RB) → v_5
  277. Vector(RO, RB) → w_5
  278. Rotate(RO, 45°, zAxis) → MD
  279. Point(g_4) → M_7
  280. Line(Z_1, P_1) → a_9
  281. Vector(MD1, LB) → w_6
  282. Vector(MD1, RO) → u_7
  283. Vector(LB, I_2) → v_7
  284. Vector(P_1, I_2) → w_7
  285. Intersect(p, q) → NN
  286. Plane(P_1, Z_1, (1, 0, 1)) → diag3
  287. Mirror(C_4, diag3) → N_7
  288. Mirror(A_4, diag3) → O_7
  289. Segment(N_7, O_7) → d_9
  290. Mirror(L_4, diag3) → P_7
  291. Mirror(M_4, diag3) → Q_7
  292. Segment(P_7, Q_7) → e_9
  293. Mirror(E_4, diag3) → R_7
  294. Mirror(D_4, diag3) → S_7
  295. Mirror(J_4, diag3) → T_7
  296. Mirror(K_4, diag3) → U_7
  297. Mirror(C_4, diag3) → V_7
  298. Mirror(O_1, diag3) → W_7
  299. Vector(O, NN) → v_2
  300. Vector(Q, NN) → u_2
  301. Segment(Z_1, LO) → j_{10}
  302. Vector(LO, MD) → v_8
  303. Vector(MD, T_4) → w_8
  304. Vector(P_1, T_4) → u_9
  305. Plane(P_1, Z_1, (1, 0, 1)) → diag4
  306. Segment(A_4, P_1) → l_5
  307. Segment(D_5, MD) → p_5
  308. Segment(P_1, MD) → g_9
  309. Segment(T_6, LO) → m_5
  310. Circle(LO, 0.2, m_5) → d_5
  311. Intersect(j_8, d_5) → B_8,
  312. Intersect(i_8, d_5) → C_8, D_8
  313. CircleArc(Z_7, E_8, A_8) → e_5
  314. CircleArc(H_8, G_8, F_8) → c_8
  315. Segment(A_4, G_8) → n_5
  316. Segment(F_8, B_8) → k_8
  317. Segment(E_8, D_8) → m_8
  318. Segment(D_5, A_8) → q_8
  319. Intersect(h_8, g_8) → I_8
  320. Segment(G_8, J_8) → t_8
  321. Segment(J_8, A_8) → a_8
  322. Segment(D_8, LO) → b_8
  323. Segment(LO, B_8) → d_8
  324. Vector(LO, MD) → v_4
  325. Vector(LO, P_1) → w_4
  326. Segment(L_6, J_8) → f_9
  327. Circle(MD, 0.2, p_5) → c_9
  328. Intersect(n_9, c_9) → K_8, L_8
  329. CircleArc(N_8, P_8, O_8) → h_9
  330. CircleArc(N_8, O_8, Q_8) → q_9
  331. Intersect(j_9, k_5) → R_8
  332. Segment(O_8, R_8) → i_9
  333. Segment(Q_8, L_8) → l_9
  334. Segment(P_8, M_8) → k_{10}
  335. Segment(M_8, P_1) → l_{10}
  336. Segment(MD, L_8) → m_{10}
  337. Segment(P_1, LO) → n_{10}
  338. Vector(MD, LO) → u_6
  339. Vector(Z_1, RB) → u_5
  340. Vector(P_1, RB) → u_8
  341. Segment(B_4, Z_1) → a_5
  342. Segment(A_4, P_1) → b_5
  343. CircleArc(S_8, T_8, V_8) → r_5
  344. Segment(V_8, U_8) → f_{10}
  345. Segment(P_1, U_8) → g_{10}
  346. CircleArc(S_8, Z_8, T_8) → c_{10}
  347. Segment(Z_8, W_8) → h_{10}
  348. Segment(W_8, Z_1) → i_{10}
  349. Segment(N_7, T_8) → p_{10}
  350. Segment(Z_1, P_1) → q_{10}
  351. Segment(Z_1, P_1) → r_{10}
  352. Vector(P_1, O_1) → v_6
  353. Segment(A_9, B_9) → s_{10}
  354. Segment(C_9, D_9) → t_{10}
  355. Segment((1, 0), (0, 1)) → a_{10}
  356. Segment(E_9, F_9) → b_{10}
  357. Sequence(y = nn, nn, 0, 7) → l1