Bull in Pipe

Bull in Pipe
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2017-07-05 21:09
This example demonstrates the geometric construction of a bull shape within a pipe, involving concepts like Binomial Distribution, Probability, Parabola, Diagrams, Dilation, Scalene Triangles, and Circle. It utilizes various GeoGebra commands such as Line, Intersect, Mirror, Midpoint, Circle, CircleArc, Segment, Point, Vector, Ray, Angle, Rotate, Translate, Polygon, OrthogonalLine, BarChart, Sequence, and If. Suitable for high school students learning geometric constructions and probability statistics.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a bull shape inside a pipe, incorporating geometric transformations like reflection, rotation, and dilation. The bull's outline consists of triangles and curves, symmetrically arranged. The pipe is a circle, and the bull's body intersects with it. Start by drawing the circular pipe, then construct the bull's head, body, and legs using geometric transformations to ensure symmetry and accuracy.
The prompt above was compiled from the original drawing commands and is for reference only.