探索体积 by Janet Bowers (2)
几何画板及绘图内容加载中,请稍等……
本范例通过填充一个盒子来验证体积公式。演示了如何使用几何画板中的命令构造几何图形,包括圆、向量、平移、旋转等。适合初中及以上学生学习立体几何。
GeoGebra 命令及参数
Circle(Origin, len - (2 * h)) → cVector((width - (2 * h), 0)) → uTranslate(A, u) → A'Intersect(c, xAxis) → B, CRotate(C, α) → C'Vector(C') → vTranslate(A, v) → A'_1Translate(A', v) → A''Polygon(A, A'_1, A'', A') → poly1, a, a'_1, a'', a'Vector((0, h)) → wTranslate(A, w) → A'_2Translate(A', w) → A''_1Translate(A'_1, w) → DTranslate(A'', w) → A'''Segment(A'_2, A) → bSegment(A''_1, A') → dSegment(D, A'_1) → eSegment(A''', A'') → fPolygon(A'_2, A''_1, A', A) → poly2, a'_2, a''_1, a'_3, a_1Polygon(D, A''', A'', A'_1) → poly3, d_1, a''', a''_2, a'_4Polygon(A''_1, A''', A'', A') → poly4, a''_3, a'''_1, a''_4, a'_5Polygon(D, A'_2, A, A'_1) → poly5, d_2, a'_6, a_2, a'_7Rotate(E, α) → E'Vector(E') → gSegment(W_1, A_2) → c_7Segment(A_2, Z_1) → d_7Segment(Z_1, V_1) → e_7Segment(V_1, W_1) → f_7Segment(Paper, U_1) → g_7Segment(U_1, S_1) → h_7Segment(S_1, T_1) → i_7Segment(T_1, Paper) → j_7OrthogonalLine(Z_1, g_7) → m_7OrthogonalLine(Z_1, h_7) → n_7OrthogonalLine(A_2, h_7) → a_8OrthogonalLine(W_1, i_7) → b_8Intersect(j_7, a_8) → B_2Intersect(i_7, b_8) → C_2Intersect(m_7, i_7) → D_2Intersect(h_7, a_8) → E_2Intersect(n_7, h_7) → F_2Intersect(m_7, g_7) → G_2Intersect(g_7, b_8) → H_2Intersect(n_7, j_7) → I_2Polygon(B_2, W_1, 4) → poly26, c_8, d_8, e_8, f_8, J_2, K_2Polygon(Paper, H_2, 4) → poly27, g_8, h_8, i_8, j_8, L_2, M_2Polygon(G_2, U_1, 4) → poly28, k_8, l_8, m_8, n_8, N_2, O_2Polygon(A_2, E_2, 4) → poly29, p_8, q_8, r_8, s_8, P_2, Q_2Polygon(V_1, Z_1, A_2, W_1) → poly31, v_1, z_1, a_9, w_1newbox(α, E, G) → n, p, c_1, e_1, f_1, g_1, h_1, i_1, j_1, k_1, J, q, H, poly6, poly7, r, s, t, b_1Intersect(r, i_1) → KIntersect(r, i_1) → LIntersect(r, e_1) → MPolygon(J, M, H, G) → poly8, j_2, m_1, h_2, g_2Polygon(B_2, W_1, V_1, I_2) → poly9, b_2, w_2, v_2, i_2Polygon(W_1, A_2, D_2, C_2) → poly10, w_3, a_3, d_3, c_2Point(w_3) → NPolygon(N, Z_1, F_2, E_2) → poly11, n_1, z_2, f_2, e_2Point(n_1) → OPoint(w_2) → PPolygon(H_2, G_2, O, P) → poly12, h_3, g_3, o, p_1blackbox(α, E, Q) → poly13, poly14, r_1, s_1, t_1, k_2, l_2, m_2, n_2, p_2, q_2, r_2, poly15, s_2, t_2, i, j, k, l, m, l_1, q_1blackbox(α, E, R) → poly16, poly17, l_3, m_3, n_3, p_3, q_3, r_3, s_3, t_3, a_4, b_4, poly18, c_4, d_4, b_3, c_3, e_3, f_3, i_3, j_3, k_3blackbox(α, E, S) → poly19, poly20, l_4, m_4, n_4, p_4, q_4, r_4, s_4, t_4, a_5, b_5, poly21, c_5, d_5, e_4, f_4, g_4, h_4, i_4, j_4, k_4blackbox(α, E, T) → poly22, poly23, l_5, m_5, n_5, p_5, q_5, r_5, s_5, t_5, a_6, b_6, poly24, c_6, d_6, e_5, f_5, g_5, h_5, i_5, j_5, k_5blackbox(α, E, U) → poly25, poly30, l_6, m_6, n_6, p_6, q_6, r_6, s_6, t_6, a_7, b_7, poly32, k_7, l_7, e_6, f_6, g_6, h_6, i_6, j_6, k_6blackbox(α, E, V) → poly33, poly34, c_9, d_9, e_9, f_9, g_9, h_9, i_9, j_9, k_9, l_9, poly35, m_9, n_9, p_7, q_7, r_7, s_7, t_7, t_8, b_9blackbox(α, E, W) → poly36, poly37, c_{10}, d_{10}, e_{10}, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, poly38, m_{10}, n_{10}, p_9, q_9, r_9, s_9, t_9, a_{10}, b_{10}blackbox(α, E, Z) → poly39, poly40, c_{11}, d_{11}, e_{11}, f_{11}, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, l_{11}, poly41, m_{11}, n_{11}, p_{10}, q_{10}, r_{10}, s_{10}, t_{10}, a_{11}, b_{11}blackbox(α, E, A_1) → poly42, poly43, c_{12}, d_{12}, e_{12}, f_{12}, g_{12}, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, poly44, m_{12}, n_{12}, p_{11}, q_{11}, r_{11}, s_{11}, t_{11}, a_{12}, b_{12}blackbox(α, E, B_1) → poly45, poly46, c_{13}, d_{13}, e_{13}, f_{13}, g_{13}, h_{13}, i_{13}, j_{13}, k_{13}, l_{13}, poly47, m_{13}, n_{13}, p_{12}, q_{12}, r_{12}, s_{12}, t_{12}, a_{13}, b_{13}blackbox(α, E, C_1) → poly48, poly49, c_{14}, d_{14}, e_{14}, f_{14}, g_{14}, h_{14}, i_{14}, j_{14}, k_{14}, l_{14}, poly50, m_{14}, n_{14}, p_{13}, q_{13}, r_{13}, s_{13}, t_{13}, a_{14}, b_{14}blackbox(α, E, D_1) → poly51, poly52, c_{15}, d_{15}, e_{15}, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, k_{15}, l_{15}, poly53, m_{15}, n_{15}, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}, a_{15}, b_{15}blackbox(α, E, E_1) → poly54, poly55, c_{16}, d_{16}, e_{16}, f_{16}, g_{16}, h_{16}, i_{16}, j_{16}, k_{16}, l_{16}, poly56, m_{16}, n_{16}, p_{15}, q_{15}, r_{15}, s_{15}, t_{15}, a_{16}, b_{16}blackbox(α, E, F_1) → poly57, poly58, c_{17}, d_{17}, e_{17}, f_{17}, g_{17}, h_{17}, i_{17}, j_{17}, k_{17}, l_{17}, poly59, m_{17}, n_{17}, p_{16}, q_{16}, r_{16}, s_{16}, t_{16}, a_{17}, b_{17}blackbox(α, E, G_1) → poly60, poly61, c_{18}, d_{18}, e_{18}, f_{18}, g_{18}, h_{18}, i_{18}, j_{18}, k_{18}, l_{18}, poly62, m_{18}, n_{18}, p_{17}, q_{17}, r_{17}, s_{17}, t_{17}, a_{18}, b_{18}