管道中的公牛

管道中的公牛
几何画板及绘图内容加载中,请稍等……
2017-07-05 21:09
①本范例演示了在管道内构建公牛形状的几何图形;②涉及的核心数学概念包括二项分布、概率、抛物线、图形、缩放、不等边三角形、圆;③作图要点——从下方『构造摘要』提炼用到了Line(线段)、Intersect(交点)、Mirror(镜像)、Midpoint(中点)、Circle(圆)、CircleArc(圆弧)、Segment(线段)、Point(点)、Vector(向量)、Ray(射线)、Angle(角度)、Rotate(旋转)、Translate(平移)、Polygon(多边形)、OrthogonalLine(垂线)、BarChart(柱状图)、Sequence(数列)、If(条件)等GeoGebra命令/对象;④适合高中阶段学习几何作图与概率统计的学生使用。

GeoGebra 命令及参数

  1. Line(S, yAxis) → g_1
  2. Intersect(g_1, i_1) → W
  3. Mirror(g_1, K') → h_1
  4. Intersect(h_1, i_1) → V
  5. Midpoint(V, W) → A
  6. Circle(K', 0.5) → r'
  7. Line(L', xAxis) → l
  8. CircleArc(A_9, B_9, C') → c
  9. Segment(A_9, E') → h
  10. Intersect(c, h, 1) → G'
  11. Segment(A_9, F') → i
  12. Intersect(c, i, 1) → H'_1
  13. CircleArc(A_9, H'_1, G') → d
  14. Point(d) → D'
  15. Vector(A_9, D') → v_7
  16. Line(K', v_7) → j
  17. Intersect(j, l) → N
  18. Ray(N, K') → t
  19. Intersect(r', t, 2) → R
  20. Line(K_1, yAxis) → l_2
  21. Line(D_1, yAxis) → q_1
  22. Vector(K', N) → n_{10}
  23. Angle(C', A_9, D') → β
  24. Rotate(D', -90°, A_9) → D'_2
  25. Vector(A_9, D'_2) → w
  26. Line(K', w) → k
  27. Intersect(k, l) → M'
  28. Line(J_1, yAxis) → k_2
  29. Line(Z, yAxis) → p_1
  30. Translate(O, n_{10}) → O'_3
  31. Ray(O, O'_3) → a_1
  32. Ray(P, O'_3) → t_1
  33. Circle(O'_3, 0.5) → e_1
  34. Intersect(e_1, t_1, 2) → F_1
  35. Intersect(e_1, a_1, 2) → E_1
  36. Polygon(K', M', O, O'_3, P, N) → poly1, k_1, m_1, o, o', p, n_1
  37. Line(F_1, o) → f_2
  38. Intersect(p_1, f_2) → G_1
  39. Line(E_1, o') → b_1
  40. Intersect(q_1, b_1) → I_1
  41. Intersect(b_1, f_2) → H_1
  42. Segment(H_1, I_1) → i_2
  43. Intersect(l_2, i_2) → M_1
  44. Vector(K', M_1) → v'
  45. Translate(A', v') → A''_1
  46. Segment(G_1, H_1) → h_2
  47. Intersect(k_2, h_2) → L_1
  48. Vector(K', L_1) → u'
  49. Translate(A', u') → A''
  50. Line(R, k_1) → f_1
  51. Intersect(f_1, p_1) → C_1
  52. Intersect(h_1, f_1) → U
  53. Translate(U, u') → U'
  54. Segment(C_1, U') → c_2
  55. Line(A''_1, c_2) → r_9
  56. Line(A'', c_2) → q_9
  57. Segment(U, C_1) → r_1
  58. Line(A', r_1) → n_9
  59. Intersect(n_9, q_9) → B'
  60. Vector(A', B') → u
  61. OrthogonalLine(K', n_1) → q
  62. Intersect(r', q, 1) → Q
  63. Line(Q, n_1) → s
  64. Intersect(s, q_1) → A_1
  65. Intersect(g_1, s) → T_7
  66. Segment(T_7, A_1) → s_1
  67. Line(A', s_1) → p_9
  68. Intersect(p_9, r_9) → A_8
  69. Vector(A', A_8) → v
  70. Angle(D'_2, A_9, D') → α
  71. Segment(A_9, D') → f
  72. Segment(A_9, D'_2) → g
  73. Rotate(D', 10°, A_9) → D'_1
  74. Vector(D'_1, D') → u_8
  75. CircleArc(A_9, D', C') → e
  76. Midpoint(A_9, D') → I'
  77. Midpoint(A_9, D'_2) → J'
  78. Segment(M', O) → m
  79. Circle(U, 1) → c_1
  80. Circle(T_7, 1) → d_1
  81. Intersect(s, f_1) → B_1
  82. Segment(U, V) → j_1
  83. Segment(T_7, W) → l_1
  84. Segment(C_1, G_1) → g_2
  85. Translate(K', u') → K'_2
  86. Translate(M', u') → M'_2
  87. Translate(O, u') → O'_1
  88. Translate(O'_3, u') → O''
  89. Translate(P, u') → P'_2
  90. Translate(N, u') → N'_2
  91. Polygon(K'_2, M'_2, O'_1, O'', P'_2, N'_2) → poly1', k', m', o'_1, o'', p', n'
  92. Translate(K', v') → K'_1
  93. Translate(M', v') → M'_1
  94. Translate(O, v') → O'_2
  95. Translate(O'_3, v') → O''_1
  96. Translate(P, v') → P'_1
  97. Translate(N, v') → N'_1
  98. Polygon(K'_1, M'_1, O'_2, O''_1, P'_1, N'_1) → poly1'_1, k'_1, m'_1, o'_2, o''_1, p'_1, n'_1
  99. Translate(K'_2, u') → K''
  100. Translate(M'_2, u') → M''
  101. Translate(O'_1, u') → N_1
  102. Translate(O'', u') → O'''
  103. Translate(P'_2, u') → P''
  104. Translate(N'_2, u') → N''
  105. Polygon(K'', M'', N_1, O''', P'', N'') → poly1'', k'', m'', n_2, o''', p'', n''
  106. Translate(K'_1, u') → O_1
  107. Translate(M'_1, u') → P_1
  108. Translate(O'_2, u') → Q_1
  109. Translate(O''_1, u') → R_1
  110. Translate(P'_1, u') → S_1
  111. Translate(N'_1, u') → T_1
  112. Polygon(O_1, P_1, Q_1, R_1, S_1, T_1) → poly2, o_1, p_2, q_2, r_2, s_2, t_2
  113. Translate(K'_1, v') → U_1
  114. Translate(M'_1, v') → V_1
  115. Translate(O'_2, v') → W_1
  116. Translate(O''_1, v') → Z_1
  117. Translate(P'_1, v') → A_2
  118. Translate(N'_1, v') → B_2
  119. Polygon(U_1, V_1, W_1, Z_1, A_2, B_2) → poly3, u_2, v_2, w_1, z_1, a_2, b_2
  120. Translate(C_1, u') → C_2
  121. Segment(U', C_2) → m_2
  122. Translate(T_7, v') → T'
  123. Translate(A_1, v') → D_2
  124. Segment(T', D_2) → d_2
  125. Segment(A_1, T') → j_2
  126. Translate(A_1, v') → E_2
  127. Translate(T', v') → T''
  128. Segment(E_2, T'') → e_2
  129. Translate(T', v') → T''_1
  130. Translate(D_2, v') → F_2
  131. Segment(T''_1, F_2) → f_3
  132. Translate(T''_1, v') → G_2
  133. Translate(F_2, v') → H_2
  134. Segment(G_2, H_2) → g_3
  135. Translate(E_2, v') → I_2
  136. Translate(T'', v') → T'''
  137. Segment(I_2, T''') → h_3
  138. Translate(C_1, u') → J_2
  139. Translate(U', u') → U''
  140. Segment(J_2, U'') → i_3
  141. Translate(U', u') → U''_1
  142. Translate(C_2, u') → K_2
  143. Segment(U''_1, K_2) → j_3
  144. Translate(U''_1, u') → L_2
  145. Translate(K_2, u') → M_2
  146. Segment(L_2, M_2) → k_3
  147. Translate(J_2, u') → N_2
  148. Translate(U'', u') → U'''
  149. Segment(N_2, U''') → l_3
  150. Translate(U_1, u') → O_2
  151. Translate(V_1, u') → P_2
  152. Translate(W_1, u') → Q_2
  153. Translate(Z_1, u') → R_2
  154. Translate(A_2, u') → S_2
  155. Translate(B_2, u') → T_2
  156. Polygon(O_2, P_2, Q_2, R_2, S_2, T_2) → poly3', o_2, p_3, q_3, r_3, s_3, t_3
  157. Translate(O_1, u') → U_2
  158. Translate(P_1, u') → V_2
  159. Translate(Q_1, u') → W_2
  160. Translate(R_1, u') → Z_2
  161. Translate(S_1, u') → A_3
  162. Translate(T_1, u') → B_3
  163. Polygon(U_2, V_2, W_2, Z_2, A_3, B_3) → poly2', u_3, v_3, w_2, z_2, a_3, b_3
  164. Translate(K'', u') → K'''
  165. Translate(M'', u') → M'''
  166. Translate(N_1, u') → C_3
  167. Translate(O''', u') → D_3
  168. Translate(P'', u') → P'''
  169. Translate(N'', u') → N'''
  170. Polygon(K''', M''', C_3, D_3, P''', N''') → poly1''', k''', m''', c_3, d_3, p''', n'''
  171. Translate(U_1, v') → E_3
  172. Translate(V_1, v') → F_3
  173. Translate(W_1, v') → G_3
  174. Translate(Z_1, v') → H_3
  175. Translate(A_2, v') → I_3
  176. Translate(B_2, v') → J_3
  177. Polygon(E_3, F_3, G_3, H_3, I_3, J_3) → poly3'_1, e_3, f_4, g_4, h_4, i_4, j_4
  178. Translate(K''', u') → K_3
  179. Translate(M''', u') → L_3
  180. Translate(C_3, u') → M_3
  181. Translate(D_3, u') → N_3
  182. Translate(P''', u') → O_3
  183. Translate(N''', u') → P_3
  184. Polygon(K_3, L_3, M_3, N_3, O_3, P_3) → poly4, k_4, l_4, m_3, n_3, o_3, p_4
  185. Translate(U_2, u') → Q_3
  186. Translate(V_2, u') → R_3
  187. Translate(W_2, u') → S_3
  188. Translate(Z_2, u') → T_3
  189. Translate(A_3, u') → U_3
  190. Translate(B_3, u') → V_3
  191. Polygon(Q_3, R_3, S_3, T_3, U_3, V_3) → poly2'', q_4, r_4, s_4, t_4, u_4, v_4
  192. Translate(O_2, u') → W_3
  193. Translate(P_2, u') → Z_3
  194. Translate(Q_2, u') → A_4
  195. Translate(R_2, u') → B_4
  196. Translate(S_2, u') → C_4
  197. Translate(T_2, u') → D_4
  198. Polygon(W_3, Z_3, A_4, B_4, C_4, D_4) → poly3'', w_3, z_3, a_4, b_4, c_4, d_4
  199. Translate(E_3, u') → E_4
  200. Translate(F_3, u') → F_4
  201. Translate(G_3, u') → G_4
  202. Translate(H_3, u') → H_4
  203. Translate(I_3, u') → I_4
  204. Translate(J_3, u') → J_4
  205. Polygon(E_4, F_4, G_4, H_4, I_4, J_4) → poly5, e_4, f_5, g_5, h_5, i_5, j_5
  206. Translate(E_3, v') → K_4
  207. Translate(F_3, v') → L_4
  208. Translate(G_3, v') → M_4
  209. Translate(H_3, v') → N_4
  210. Translate(I_3, v') → O_4
  211. Translate(J_3, v') → P_4
  212. Polygon(K_4, L_4, M_4, N_4, O_4, P_4) → poly6, k_5, l_5, m_4, n_4, o_4, p_5
  213. Translate(L_2, u') → Q_4
  214. Translate(M_2, u') → R_4
  215. Segment(Q_4, R_4) → m_5
  216. Translate(N_2, u') → S_4
  217. Translate(U''', u') → T_4
  218. Segment(S_4, T_4) → n_5
  219. Translate(Q_4, u') → U_4
  220. Translate(R_4, u') → V_4
  221. Segment(U_4, V_4) → q_5
  222. Translate(S_4, u') → W_4
  223. Translate(T_4, u') → Z_4
  224. Segment(W_4, Z_4) → r_5
  225. Translate(G_2, v') → A_5
  226. Translate(H_2, v') → B_5
  227. Segment(A_5, B_5) → s_5
  228. Translate(I_2, v') → C_5
  229. Translate(T''', v') → D_5
  230. Segment(C_5, D_5) → t_5
  231. Translate(A_5, v') → E_5
  232. Translate(B_5, v') → F_5
  233. Segment(E_5, F_5) → a_5
  234. Translate(C_5, v') → G_5
  235. Translate(D_5, v') → H_5
  236. Segment(G_5, H_5) → b_5
  237. Translate(P_4, v') → I_5
  238. Translate(K_4, v') → J_5
  239. Segment(I_5, J_5) → c_5
  240. Translate(K_4, v') → K_5
  241. Translate(L_4, v') → L_5
  242. Segment(K_5, L_5) → d_5
  243. Translate(J_4, v') → M_5
  244. Translate(E_4, v') → N_5
  245. Segment(M_5, N_5) → e_5
  246. Translate(E_4, v') → O_5
  247. Translate(F_4, v') → P_5
  248. Segment(O_5, P_5) → f_6
  249. Translate(D_4, v') → Q_5
  250. Translate(W_3, v') → R_5
  251. Segment(Q_5, R_5) → g_6
  252. Translate(W_3, v') → S_5
  253. Translate(Z_3, v') → T_5
  254. Segment(S_5, T_5) → h_6
  255. Translate(V_3, v') → U_5
  256. Translate(Q_3, v') → V_5
  257. Segment(U_5, V_5) → i_6
  258. Translate(Q_3, v') → W_5
  259. Translate(R_3, v') → Z_5
  260. Segment(W_5, Z_5) → j_6
  261. Translate(P_3, v') → A_6
  262. Translate(K_3, v') → B_6
  263. Segment(A_6, B_6) → k_6
  264. Translate(K_3, v') → C_6
  265. Translate(L_3, v') → D_6
  266. Segment(C_6, D_6) → l_6
  267. Translate(P_3, u') → E_6
  268. Translate(K_3, u') → F_6
  269. Segment(E_6, F_6) → m_6
  270. Translate(K_3, u') → G_6
  271. Translate(L_3, u') → H_6
  272. Segment(G_6, H_6) → n_6
  273. Line(V_4, yAxis) → q_6
  274. Line(H_6, yAxis) → r_6
  275. Line(D_6, yAxis) → s_6
  276. Line(D_6, yAxis) → t_6
  277. Line(E_6, yAxis) → a_6
  278. Line(Z_5, t_6) → b_6
  279. Line(A_6, t_6) → c_6
  280. Line(U_5, t_6) → d_6
  281. Line(T_5, b_6) → e_6
  282. Line(Q_5, e_6) → f_7
  283. Line(P_5, f_7) → g_7
  284. Line(M_5, g_7) → h_7
  285. Line(L_5, h_7) → i_7
  286. Line(I_5, h_7) → j_7
  287. Line(F_5, i_7) → k_7
  288. Intersect(p_6, q_6) → I_6
  289. Intersect(p_6, r_6) → J_6
  290. Intersect(p_6, a_6) → K_6
  291. Intersect(p_6, s_6) → L_6
  292. Intersect(p_6, c_6) → M_6
  293. Intersect(p_6, b_6) → N_6
  294. Intersect(p_6, d_6) → O_6
  295. Intersect(p_6, e_6) → P_6
  296. Intersect(p_6, f_7) → Q_6
  297. Intersect(p_6, g_7) → R_6
  298. Intersect(p_6, h_7) → S_6
  299. Intersect(p_6, i_7) → T_6
  300. Intersect(p_6, j_7) → U_6
  301. Intersect(p_6, k_7) → V_6
  302. Segment(V_4, I_6) → l_7
  303. Segment(H_6, J_6) → m_7
  304. Segment(E_6, K_6) → n_7
  305. Segment(D_6, L_6) → p_7
  306. Segment(A_6, M_6) → q_7
  307. Segment(Z_5, N_6) → r_7
  308. Segment(U_5, O_6) → s_7
  309. Segment(T_5, P_6) → t_7
  310. Segment(Q_5, Q_6) → a_7
  311. Segment(P_5, R_6) → b_7
  312. Segment(M_5, S_6) → c_7
  313. Segment(L_5, T_6) → d_7
  314. Segment(I_5, U_6) → e_7
  315. Segment(F_5, V_6) → f_8
  316. Segment(I_6, J_6) → g_8
  317. Segment(K_6, L_6) → h_8
  318. Segment(M_6, N_6) → i_8
  319. Segment(O_6, P_6) → j_8
  320. Segment(Q_6, R_6) → k_8
  321. Segment(S_6, T_6) → l_8
  322. Segment(U_6, V_6) → m_8
  323. Polygon(U_6, L_7, M_7, V_6) → poly7, u_6, l_9, m_9, v_6
  324. Polygon(S_6, T_6, K_7, J_7) → poly8, s_8, t_8, k_9, j_9
  325. Polygon(Q_6, R_6, I_7, G_7) → poly9, q_8, r_8, i_9, g_9
  326. Polygon(O_6, P_6, F_7, E_7) → poly10, o_6, p_8, f_9, e_8
  327. Polygon(M_6, N_6, D_7, C_7) → poly11, m_{10}, n_8, d_8, c_8
  328. Polygon(K_6, L_6, B_7, A_7) → poly12, k_{10}, l_{10}, b_8, a_8
  329. Polygon(I_6, J_6, Z_6, W_6) → poly13, i_{10}, j_{10}, z_6, w_6
  330. Midpoint(z_6) → H'
  331. Midpoint(b_8) → N'
  332. Midpoint(d_8) → O'
  333. Midpoint(f_9) → P'
  334. Midpoint(i_9) → Q'
  335. Midpoint(k_9) → R'
  336. Midpoint(l_9) → S'
  337. Circle(K', 0.25) → d_9
  338. Intersect(d_9, k) → V_7, W_7
  339. Intersect(d_9, t) → U_7, Z_7
  340. BarChart({x(H'), x(N'), x(O'), x(P'), x(Q'), x(R'), x(S')}, {n1, n2, n3, n4, n5, n6, n7}, 0.5) → u_1
  341. Circle(A, 0.15) → c_9
  342. BarChart({x(H'), x(N'), x(O'), x(P'), x(Q'), x(R'), x(S')}, {((2 * u_1) * a0), ((2 * u_1) * a1), ((2 * u_1) * a2), ((2 * u_1) * a3), ((2 * u_1) * a4), ((2 * u_1) * a5), ((2 * u_1) * a6)}, 0.5) → o_5
  343. Sequence(Text[Element[a, k], (x(Element[T, k]) - 0.2, ((2 * u_1) * Element[a, k]) + 0.1)], k, 1, 7) → list2
  344. Sequence(Text[Element[n, k] / ((2 * u_1)), (x(Element[T, k]) + 0.3, Element[n, k])], k, 1, 7) → list1
  345. Sequence(Text[Element[a, k], (x(Element[T, k]) - 0.2, (2 * Element[a, k]) + 0.1)], k, 1, 7) → list3
  346. BarChart({x(H'), x(N'), x(O'), x(P'), x(Q'), x(R'), x(S')}, {(2 * a0), (2 * a1), (2 * a2), (2 * a3), (2 * a4), (2 * a5), (2 * a6)}, 0.5) → u_5
  347. If(random() < a', A' + u', A' + v') → B
  348. If(random() < a', B + u', B + v') → C
  349. If(random() < a', C + u', C + v') → D
  350. If(random() < a', D + u', D + v') → E
  351. If(random() < a', E + u', E + v') → F
  352. If(random() < a', F + u', F + v') → G

AI 绘图提示语参考

画一个牛形图案,包含一个圆形管道和牛的轮廓。牛的轮廓由多个三角形和曲线组成,通过镜像、旋转和缩放等变换得到。管道是一个圆形,牛的轮廓与管道内部相交。首先画出管道,然后逐步构建牛的头部、身体和腿部,注意使用对称和几何变换来确保形状的准确性。
以上提示语为根据原始绘图命令整理而来,仅供参考。