Bull in Pipe
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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
Line(S, yAxis) → g_1Intersect(g_1, i_1) → WMirror(g_1, K') → h_1Intersect(h_1, i_1) → VMidpoint(V, W) → ACircle(K', 0.5) → r'Line(L', xAxis) → lCircleArc(A_9, B_9, C') → cSegment(A_9, E') → hIntersect(c, h, 1) → G'Segment(A_9, F') → iIntersect(c, i, 1) → H'_1CircleArc(A_9, H'_1, G') → dPoint(d) → D'Vector(A_9, D') → v_7Line(K', v_7) → jIntersect(j, l) → NRay(N, K') → tIntersect(r', t, 2) → RLine(K_1, yAxis) → l_2Line(D_1, yAxis) → q_1Vector(K', N) → n_{10}Angle(C', A_9, D') → βRotate(D', -90°, A_9) → D'_2Vector(A_9, D'_2) → wLine(K', w) → kIntersect(k, l) → M'Line(J_1, yAxis) → k_2Line(Z, yAxis) → p_1Translate(O, n_{10}) → O'_3Ray(O, O'_3) → a_1Ray(P, O'_3) → t_1Circle(O'_3, 0.5) → e_1Intersect(e_1, t_1, 2) → F_1Intersect(e_1, a_1, 2) → E_1Polygon(K', M', O, O'_3, P, N) → poly1, k_1, m_1, o, o', p, n_1Line(F_1, o) → f_2Intersect(p_1, f_2) → G_1Line(E_1, o') → b_1Intersect(q_1, b_1) → I_1Intersect(b_1, f_2) → H_1Segment(H_1, I_1) → i_2Intersect(l_2, i_2) → M_1Vector(K', M_1) → v'Translate(A', v') → A''_1Segment(G_1, H_1) → h_2Intersect(k_2, h_2) → L_1Vector(K', L_1) → u'Translate(A', u') → A''Line(R, k_1) → f_1Intersect(f_1, p_1) → C_1Intersect(h_1, f_1) → UTranslate(U, u') → U'Segment(C_1, U') → c_2Line(A''_1, c_2) → r_9Line(A'', c_2) → q_9Segment(U, C_1) → r_1Line(A', r_1) → n_9Intersect(n_9, q_9) → B'Vector(A', B') → uOrthogonalLine(K', n_1) → qIntersect(r', q, 1) → QLine(Q, n_1) → sIntersect(s, q_1) → A_1Intersect(g_1, s) → T_7Segment(T_7, A_1) → s_1Line(A', s_1) → p_9Intersect(p_9, r_9) → A_8Vector(A', A_8) → vAngle(D'_2, A_9, D') → αSegment(A_9, D') → fSegment(A_9, D'_2) → gRotate(D', 10°, A_9) → D'_1Vector(D'_1, D') → u_8CircleArc(A_9, D', C') → eMidpoint(A_9, D') → I'Midpoint(A_9, D'_2) → J'Segment(M', O) → mCircle(U, 1) → c_1Circle(T_7, 1) → d_1Intersect(s, f_1) → B_1Segment(U, V) → j_1Segment(T_7, W) → l_1Segment(C_1, G_1) → g_2Translate(K', u') → K'_2Translate(M', u') → M'_2Translate(O, u') → O'_1Translate(O'_3, u') → O''Translate(P, u') → P'_2Translate(N, u') → N'_2Polygon(K'_2, M'_2, O'_1, O'', P'_2, N'_2) → poly1', k', m', o'_1, o'', p', n'Translate(K', v') → K'_1Translate(M', v') → M'_1Translate(O, v') → O'_2Translate(O'_3, v') → O''_1Translate(P, v') → P'_1Translate(N, v') → N'_1Polygon(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'_1Translate(K'_2, u') → K''Translate(M'_2, u') → M''Translate(O'_1, u') → N_1Translate(O'', u') → O'''Translate(P'_2, u') → P''Translate(N'_2, u') → N''Polygon(K'', M'', N_1, O''', P'', N'') → poly1'', k'', m'', n_2, o''', p'', n''Translate(K'_1, u') → O_1Translate(M'_1, u') → P_1Translate(O'_2, u') → Q_1Translate(O''_1, u') → R_1Translate(P'_1, u') → S_1Translate(N'_1, u') → T_1Polygon(O_1, P_1, Q_1, R_1, S_1, T_1) → poly2, o_1, p_2, q_2, r_2, s_2, t_2Translate(K'_1, v') → U_1Translate(M'_1, v') → V_1Translate(O'_2, v') → W_1Translate(O''_1, v') → Z_1Translate(P'_1, v') → A_2Translate(N'_1, v') → B_2Polygon(U_1, V_1, W_1, Z_1, A_2, B_2) → poly3, u_2, v_2, w_1, z_1, a_2, b_2Translate(C_1, u') → C_2Segment(U', C_2) → m_2Translate(T_7, v') → T'Translate(A_1, v') → D_2Segment(T', D_2) → d_2Segment(A_1, T') → j_2Translate(A_1, v') → E_2Translate(T', v') → T''Segment(E_2, T'') → e_2Translate(T', v') → T''_1Translate(D_2, v') → F_2Segment(T''_1, F_2) → f_3Translate(T''_1, v') → G_2Translate(F_2, v') → H_2Segment(G_2, H_2) → g_3Translate(E_2, v') → I_2Translate(T'', v') → T'''Segment(I_2, T''') → h_3Translate(C_1, u') → J_2Translate(U', u') → U''Segment(J_2, U'') → i_3Translate(U', u') → U''_1Translate(C_2, u') → K_2Segment(U''_1, K_2) → j_3Translate(U''_1, u') → L_2Translate(K_2, u') → M_2Segment(L_2, M_2) → k_3Translate(J_2, u') → N_2Translate(U'', u') → U'''Segment(N_2, U''') → l_3Translate(U_1, u') → O_2Translate(V_1, u') → P_2Translate(W_1, u') → Q_2Translate(Z_1, u') → R_2Translate(A_2, u') → S_2Translate(B_2, u') → T_2Polygon(O_2, P_2, Q_2, R_2, S_2, T_2) → poly3', o_2, p_3, q_3, r_3, s_3, t_3Translate(O_1, u') → U_2Translate(P_1, u') → V_2Translate(Q_1, u') → W_2Translate(R_1, u') → Z_2Translate(S_1, u') → A_3Translate(T_1, u') → B_3Polygon(U_2, V_2, W_2, Z_2, A_3, B_3) → poly2', u_3, v_3, w_2, z_2, a_3, b_3Translate(K'', u') → K'''Translate(M'', u') → M'''Translate(N_1, u') → C_3Translate(O''', u') → D_3Translate(P'', u') → P'''Translate(N'', u') → N'''Polygon(K''', M''', C_3, D_3, P''', N''') → poly1''', k''', m''', c_3, d_3, p''', n'''Translate(U_1, v') → E_3Translate(V_1, v') → F_3Translate(W_1, v') → G_3Translate(Z_1, v') → H_3Translate(A_2, v') → I_3Translate(B_2, v') → J_3Polygon(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_4Translate(K''', u') → K_3Translate(M''', u') → L_3Translate(C_3, u') → M_3Translate(D_3, u') → N_3Translate(P''', u') → O_3Translate(N''', u') → P_3Polygon(K_3, L_3, M_3, N_3, O_3, P_3) → poly4, k_4, l_4, m_3, n_3, o_3, p_4Translate(U_2, u') → Q_3Translate(V_2, u') → R_3Translate(W_2, u') → S_3Translate(Z_2, u') → T_3Translate(A_3, u') → U_3Translate(B_3, u') → V_3Polygon(Q_3, R_3, S_3, T_3, U_3, V_3) → poly2'', q_4, r_4, s_4, t_4, u_4, v_4Translate(O_2, u') → W_3Translate(P_2, u') → Z_3Translate(Q_2, u') → A_4Translate(R_2, u') → B_4Translate(S_2, u') → C_4Translate(T_2, u') → D_4Polygon(W_3, Z_3, A_4, B_4, C_4, D_4) → poly3'', w_3, z_3, a_4, b_4, c_4, d_4Translate(E_3, u') → E_4Translate(F_3, u') → F_4Translate(G_3, u') → G_4Translate(H_3, u') → H_4Translate(I_3, u') → I_4Translate(J_3, u') → J_4Polygon(E_4, F_4, G_4, H_4, I_4, J_4) → poly5, e_4, f_5, g_5, h_5, i_5, j_5Translate(E_3, v') → K_4Translate(F_3, v') → L_4Translate(G_3, v') → M_4Translate(H_3, v') → N_4Translate(I_3, v') → O_4Translate(J_3, v') → P_4Polygon(K_4, L_4, M_4, N_4, O_4, P_4) → poly6, k_5, l_5, m_4, n_4, o_4, p_5Translate(L_2, u') → Q_4Translate(M_2, u') → R_4Segment(Q_4, R_4) → m_5Translate(N_2, u') → S_4Translate(U''', u') → T_4Segment(S_4, T_4) → n_5Translate(Q_4, u') → U_4Translate(R_4, u') → V_4Segment(U_4, V_4) → q_5Translate(S_4, u') → W_4Translate(T_4, u') → Z_4Segment(W_4, Z_4) → r_5Translate(G_2, v') → A_5Translate(H_2, v') → B_5Segment(A_5, B_5) → s_5Translate(I_2, v') → C_5Translate(T''', v') → D_5Segment(C_5, D_5) → t_5Translate(A_5, v') → E_5Translate(B_5, v') → F_5Segment(E_5, F_5) → a_5Translate(C_5, v') → G_5Translate(D_5, v') → H_5Segment(G_5, H_5) → b_5Translate(P_4, v') → I_5Translate(K_4, v') → J_5Segment(I_5, J_5) → c_5Translate(K_4, v') → K_5Translate(L_4, v') → L_5Segment(K_5, L_5) → d_5Translate(J_4, v') → M_5Translate(E_4, v') → N_5Segment(M_5, N_5) → e_5Translate(E_4, v') → O_5Translate(F_4, v') → P_5Segment(O_5, P_5) → f_6Translate(D_4, v') → Q_5Translate(W_3, v') → R_5Segment(Q_5, R_5) → g_6Translate(W_3, v') → S_5Translate(Z_3, v') → T_5Segment(S_5, T_5) → h_6Translate(V_3, v') → U_5Translate(Q_3, v') → V_5Segment(U_5, V_5) → i_6Translate(Q_3, v') → W_5Translate(R_3, v') → Z_5Segment(W_5, Z_5) → j_6Translate(P_3, v') → A_6Translate(K_3, v') → B_6Segment(A_6, B_6) → k_6Translate(K_3, v') → C_6Translate(L_3, v') → D_6Segment(C_6, D_6) → l_6Translate(P_3, u') → E_6Translate(K_3, u') → F_6Segment(E_6, F_6) → m_6Translate(K_3, u') → G_6Translate(L_3, u') → H_6Segment(G_6, H_6) → n_6Line(V_4, yAxis) → q_6Line(H_6, yAxis) → r_6Line(D_6, yAxis) → s_6Line(D_6, yAxis) → t_6Line(E_6, yAxis) → a_6Line(Z_5, t_6) → b_6Line(A_6, t_6) → c_6Line(U_5, t_6) → d_6Line(T_5, b_6) → e_6Line(Q_5, e_6) → f_7Line(P_5, f_7) → g_7Line(M_5, g_7) → h_7Line(L_5, h_7) → i_7Line(I_5, h_7) → j_7Line(F_5, i_7) → k_7Intersect(p_6, q_6) → I_6Intersect(p_6, r_6) → J_6Intersect(p_6, a_6) → K_6Intersect(p_6, s_6) → L_6Intersect(p_6, c_6) → M_6Intersect(p_6, b_6) → N_6Intersect(p_6, d_6) → O_6Intersect(p_6, e_6) → P_6Intersect(p_6, f_7) → Q_6Intersect(p_6, g_7) → R_6Intersect(p_6, h_7) → S_6Intersect(p_6, i_7) → T_6Intersect(p_6, j_7) → U_6Intersect(p_6, k_7) → V_6Segment(V_4, I_6) → l_7Segment(H_6, J_6) → m_7Segment(E_6, K_6) → n_7Segment(D_6, L_6) → p_7Segment(A_6, M_6) → q_7Segment(Z_5, N_6) → r_7Segment(U_5, O_6) → s_7Segment(T_5, P_6) → t_7Segment(Q_5, Q_6) → a_7Segment(P_5, R_6) → b_7Segment(M_5, S_6) → c_7Segment(L_5, T_6) → d_7Segment(I_5, U_6) → e_7Segment(F_5, V_6) → f_8Segment(I_6, J_6) → g_8Segment(K_6, L_6) → h_8Segment(M_6, N_6) → i_8Segment(O_6, P_6) → j_8Segment(Q_6, R_6) → k_8Segment(S_6, T_6) → l_8Segment(U_6, V_6) → m_8Polygon(U_6, L_7, M_7, V_6) → poly7, u_6, l_9, m_9, v_6Polygon(S_6, T_6, K_7, J_7) → poly8, s_8, t_8, k_9, j_9Polygon(Q_6, R_6, I_7, G_7) → poly9, q_8, r_8, i_9, g_9Polygon(O_6, P_6, F_7, E_7) → poly10, o_6, p_8, f_9, e_8Polygon(M_6, N_6, D_7, C_7) → poly11, m_{10}, n_8, d_8, c_8Polygon(K_6, L_6, B_7, A_7) → poly12, k_{10}, l_{10}, b_8, a_8Polygon(I_6, J_6, Z_6, W_6) → poly13, i_{10}, j_{10}, z_6, w_6Midpoint(z_6) → H'Midpoint(b_8) → N'Midpoint(d_8) → O'Midpoint(f_9) → P'Midpoint(i_9) → Q'Midpoint(k_9) → R'Midpoint(l_9) → S'Circle(K', 0.25) → d_9Intersect(d_9, k) → V_7, W_7Intersect(d_9, t) → U_7, Z_7BarChart({x(H'), x(N'), x(O'), x(P'), x(Q'), x(R'), x(S')}, {n1, n2, n3, n4, n5, n6, n7}, 0.5) → u_1Circle(A, 0.15) → c_9BarChart({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_5Sequence(Text[Element[a, k], (x(Element[T, k]) - 0.2, ((2 * u_1) * Element[a, k]) + 0.1)], k, 1, 7) → list2Sequence(Text[Element[n, k] / ((2 * u_1)), (x(Element[T, k]) + 0.3, Element[n, k])], k, 1, 7) → list1Sequence(Text[Element[a, k], (x(Element[T, k]) - 0.2, (2 * Element[a, k]) + 0.1)], k, 1, 7) → list3BarChart({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_5If(random() < a', A' + u', A' + v') → BIf(random() < a', B + u', B + v') → CIf(random() < a', C + u', C + v') → DIf(random() < a', D + u', D + v') → EIf(random() < a', E + u', E + v') → FIf(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.