长方体 by KruPongsak Wuttisant _TH
几何画板及绘图内容加载中,请稍等……
这个范例演示了长方体的构造及其展开图。核心数学概念包括立体几何中的长方体性质。通过使用GeoGebra命令如Polygon、Prism、Net等,可以直观地展示长方体的各个面和边。适合初中及以上学生学习立体几何。
GeoGebra 命令及参数
Polygon(A, B, C, D) → q1, a_1, b_1, c_1, dPrism(q1, c) → e, E, ขอบAE, ขอบBF, ขอบCG, ขอบDH, ขอบEF, ขอบFG, ขอบGH, ขอบEH, F, G, H, หน้าABFE, หน้าBCGF, หน้าCDHG, หน้าADHE, หน้าEFGHNet(e, g) → f, I, R, S, T, U, V, face1, face2, face3, face4, face5, J, face6, ขอบ1, ขอบ2, ขอบ3, ขอบ4, ขอบ5, ขอบ6, ขอบ7, ขอบ8, ขอบ9, K, ขอบ10, ขอบ11, ขอบ12, ขอบ13, ขอบ14, ขอบ15, ขอบ16, ขอบ17, ขอบ18, ขอบ19, L, M, N, O, P, QCircle(A, 1, ขอบ4) → hIntersect(ขอบ1, h, 1) → A_1Vector(A, A_1) → uTranslate(L, u) → L'Translate(I, u) → I'Segment(L', I') → ขอบ4'Translate(L', u) → L''Translate(I', u) → I''Segment(L'', I'') → ขอบ4''Translate(L'', u) → L'''Translate(I'', u) → I'''Segment(L''', I''') → ขอบ4'''Translate(L''', u) → ZTranslate(I''', u) → B_1Segment(Z, B_1) → iTranslate(Z, u) → Z'Translate(B_1, u) → C_1Segment(Z', C_1) → i'Translate(Z', u) → Z''Translate(C_1, u) → D_1Segment(Z'', D_1) → i''Translate(Z'', u) → Z'''Translate(D_1, u) → E_1Segment(Z''', E_1) → i'''Translate(Z''', u) → F_1Translate(E_1, u) → G_1Segment(F_1, G_1) → jTranslate(K, u) → K'Translate(K', u) → K''Translate(F_1, u) → H_1Translate(G_1, u) → I_1Segment(H_1, I_1) → j'Translate(H_1, u) → J_1Translate(I_1, u) → K_1Segment(J_1, K_1) → j''Translate(J_1, u) → L_1Translate(K_1, u) → M_1Segment(L_1, M_1) → j'''Point(ขอบ16) → N_1Circle(C, 1, ขอบ3) → kIntersect(ขอบ11, k) → W, Q_1Vector(C, Q_1) → vTranslate(K, v) → K'_1Translate(L, v) → L'_1Segment(K'_1, L'_1) → ขอบ3'Translate(K'_1, v) → R_1Translate(L'_1, v) → S_1Segment(R_1, S_1) → ขอบ3''Translate(R_1, v) → T_1Translate(S_1, v) → U_1Segment(T_1, U_1) → ขอบ3'''Translate(T_1, v) → V_1Translate(U_1, v) → W_1Segment(V_1, W_1) → lTranslate(V_1, v) → Z_1Translate(W_1, v) → A_2Segment(Z_1, A_2) → l'Translate(Z_1, v) → B_2Translate(A_2, v) → C_2Segment(B_2, C_2) → l''Translate(B_2, v) → D_2Translate(C_2, v) → E_2Segment(D_2, E_2) → l'''Translate(D_2, v) → F_2Translate(E_2, v) → G_2Segment(F_2, G_2) → mTranslate(F_2, v) → H_2Translate(G_2, v) → I_2Segment(H_2, I_2) → m'Translate(H_2, v) → J_2Translate(H_2, v) → K_2Translate(H_2, v) → L_2Translate(I_2, v) → M_2Segment(L_2, M_2) → m''Translate(L_2, v) → N_2Translate(M_2, v) → O_2Segment(N_2, O_2) → m'''Translate(L, u) → L'_2Translate(R, u) → R'Segment(L'_2, R') → ขอบ13'Translate(L'_2, u) → P_2Translate(R', u) → R''Segment(P_2, R'') → ขอบ13''Translate(P_2, u) → Q_2Translate(R'', u) → R'''Segment(Q_2, R''') → ขอบ13'''Translate(Q_2, u) → R_2Translate(R''', u) → S_2Segment(R_2, S_2) → nTranslate(R_2, u) → T_2Translate(S_2, u) → U_2Segment(T_2, U_2) → n'Translate(T_2, u) → V_2Translate(U_2, u) → W_2Segment(V_2, W_2) → n''Translate(V_2, u) → Z_2Translate(W_2, u) → A_3Segment(Z_2, A_3) → n'''Translate(Z_2, u) → B_3Translate(A_3, u) → C_3Segment(B_3, C_3) → pTranslate(B_3, u) → D_3Translate(C_3, u) → E_3Segment(D_3, E_3) → p'Translate(D_3, u) → F_3Translate(E_3, u) → G_3Segment(F_3, G_3) → p''Translate(F_3, u) → H_3Translate(G_3, u) → I_3Segment(H_3, I_3) → p'''Circle(B, 1, ขอบ1) → rIntersect(ขอบ7, r) → K_3,Vector(B, K_3) → sTranslate(I, s) → I'_1Translate(J, s) → J'Segment(I'_1, J') → ขอบ1'Translate(I'_1, s) → L_3Translate(J', s) → J''Segment(L_3, J'') → ขอบ1''Translate(L_3, s) → M_3Translate(J'', s) → J'''Segment(M_3, J''') → ขอบ1'''Translate(M_3, s) → N_3Translate(J''', s) → O_3Segment(N_3, O_3) → tTranslate(N_3, s) → P_3Translate(O_3, s) → Q_3Segment(P_3, Q_3) → t'Translate(P_3, s) → R_3Translate(Q_3, s) → S_3Segment(R_3, S_3) → t''Translate(R_3, s) → T_3Translate(S_3, s) → U_3Segment(T_3, U_3) → t'''Translate(T_3, s) → V_3Translate(U_3, s) → W_3Segment(V_3, W_3) → f_1Translate(V_3, s) → Z_3Translate(W_3, s) → A_4Segment(Z_3, A_4) → g_1Translate(Z_3, s) → B_4Translate(A_4, s) → C_4Segment(B_4, C_4) → h_1Translate(B_4, s) → D_4Translate(C_4, s) → E_4Segment(D_4, E_4) → i_1Intersect(ขอบ2, r, 1) → F_4Circle(N, 1, ขอบ6) → qIntersect(ขอบ17, q, 1) → J_3Vector(N, J_3) → u_1Translate(N, u_1) → N'Translate(M, u_1) → M'Segment(N', M') → ขอบ6'Translate(N', u_1) → N''Translate(M', u_1) → M''Segment(N'', M'') → ขอบ6''Translate(N'', u_1) → N'''Translate(M'', u_1) → M'''Segment(N''', M''') → ขอบ6'''Translate(N''', u_1) → G_4Translate(M''', u_1) → H_4Segment(G_4, H_4) → j_1Translate(G_4, u_1) → I_4Translate(H_4, u_1) → J_4Segment(I_4, J_4) → k_1Translate(I_4, u_1) → K_4Translate(J_4, u_1) → L_4Segment(K_4, L_4) → l_1Translate(K_4, u_1) → M_4Translate(L_4, u_1) → N_4Segment(M_4, N_4) → m_1Translate(M_4, u_1) → O_4Translate(N_4, u_1) → P_4Segment(O_4, P_4) → n_1Translate(O_4, u_1) → Q_4Translate(P_4, u_1) → R_4Segment(Q_4, R_4) → p_1Translate(Q_4, u_1) → S_4Translate(R_4, u_1) → T_4Segment(S_4, T_4) → q_1Translate(S_4, u_1) → U_4Translate(T_4, u_1) → V_4Segment(U_4, V_4) → r_1Vector(B, F_4) → v_1Translate(I, v_1) → I'_2Translate(J, v_1) → J'_1Segment(I'_2, J'_1) → ขอบ1'_1Translate(I'_2, v_1) → W_4Translate(J'_1, v_1) → Z_4Segment(W_4, Z_4) → s_1Translate(W_4, v_1) → A_5Translate(Z_4, v_1) → B_5Segment(A_5, B_5) → t_1Translate(A_5, v_1) → C_5Translate(B_5, v_1) → D_5Segment(C_5, D_5) → d_1Translate(C_5, v_1) → E_5Translate(D_5, v_1) → F_5Segment(E_5, F_5) → e_1Translate(E_5, v_1) → G_5Translate(F_5, v_1) → H_5Segment(G_5, H_5) → f_2Translate(G_5, v_1) → I_5Translate(H_5, v_1) → J_5Segment(I_5, J_5) → g_2Translate(I_5, v_1) → K_5Translate(J_5, v_1) → L_5Segment(K_5, L_5) → h_2Translate(K_5, v_1) → M_5Translate(L_5, v_1) → N_5Segment(M_5, N_5) → i_2Translate(M_5, v_1) → O_5Translate(N_5, v_1) → P_5Translate(O_5, v_1) → Q_5Translate(P_5, v_1) → R_5Segment(Q_5, R_5) → k_2Translate(M, u) → M'_1Translate(I, u) → I'_3Segment(M'_1, I'_3) → ขอบ5'Translate(M'_1, u) → S_5Translate(I'_3, u) → T_5Segment(S_5, T_5) → ขอบ5''Translate(S_5, u) → U_5Translate(T_5, u) → V_5Segment(U_5, V_5) → ขอบ5'''Translate(U_5, u) → W_5Translate(V_5, u) → Z_5Segment(W_5, Z_5) → l_2Translate(W_5, u) → A_6Translate(Z_5, u) → B_6Segment(A_6, B_6) → m_2Translate(A_6, u) → C_6Translate(B_6, u) → D_6Segment(C_6, D_6) → n_2Translate(C_6, u) → E_6Translate(D_6, u) → F_6Segment(E_6, F_6) → p_2Translate(E_6, u) → G_6Translate(F_6, u) → H_6Segment(G_6, H_6) → q_2Translate(G_6, u) → I_6Translate(H_6, u) → J_6Segment(I_6, J_6) → r_2Translate(I_6, u) → K_6Translate(J_6, u) → L_6Segment(K_6, L_6) → s_2Segment(M, V) → t_2Translate(M, u) → M'_2Translate(V, u) → V'Segment(M'_2, V') → a_2Translate(M'_2, u) → M_6Translate(V', u) → V''Segment(M_6, V'') → b_2Translate(M_6, u) → N_6Translate(V'', u) → V'''Segment(N_6, V''') → c_2Translate(N_6, u) → O_6Translate(V''', u) → P_6Segment(O_6, P_6) → d_2Translate(O_6, u) → Q_6Translate(P_6, u) → R_6Segment(Q_6, R_6) → e_2Translate(Q_6, u) → S_6Translate(R_6, u) → T_6Segment(S_6, T_6) → f_3Translate(S_6, u) → U_6Translate(T_6, u) → V_6Segment(U_6, V_6) → g_3Translate(U_6, u) → W_6Translate(V_6, u) → Z_6Segment(W_6, Z_6) → h_3Translate(W_6, u) → A_7Translate(Z_6, u) → B_7Segment(A_7, B_7) → i_3Translate(A_7, u) → C_7Translate(B_7, u) → D_7Segment(C_7, D_7) → j_3Translate(C_7, u) → E_7Translate(D_7, u) → F_7Segment(E_7, F_7) → k_3Translate(K_6, u) → G_7Translate(L_6, u) → H_7Segment(G_7, H_7) → l_3Circle(C, 1, ขอบ2) → c_3Intersect(ขอบ10, c_3) → I_7,Vector(C, I_7) → w_1Translate(J, w_1) → J'_2Translate(K, w_1) → K'_2Segment(J'_2, K'_2) → ขอบ2'Translate(J'_2, w_1) → J_7Translate(K'_2, w_1) → K_7Segment(J_7, K_7) → ขอบ2''Translate(J_7, w_1) → L_7Translate(K_7, w_1) → M_7Segment(L_7, M_7) → ขอบ2'''Translate(L_7, w_1) → N_7Translate(M_7, w_1) → O_7Segment(N_7, O_7) → j_2Translate(N_7, w_1) → P_7Translate(O_7, w_1) → Q_7Segment(P_7, Q_7) → m_3Translate(P_7, w_1) → R_7Translate(Q_7, w_1) → S_7Segment(R_7, S_7) → n_3Translate(R_7, w_1) → T_7Translate(S_7, w_1) → U_7Segment(T_7, U_7) → p_3Translate(T_7, w_1) → V_7Translate(U_7, w_1) → W_7Segment(V_7, W_7) → q_3Translate(V_7, w_1) → Z_7Translate(W_7, w_1) → A_8Segment(Z_7, A_8) → r_3Intersect(ขอบ16, h, 1) → B_8Vector(A, B_8) → u_2Translate(L, u_2) → L'_3Translate(I, u_2) → I'_4Segment(L'_3, I'_4) → ขอบ4'_1Translate(L'_3, u_2) → C_8Translate(I'_4, u_2) → D_8Segment(C_8, D_8) → s_3Translate(C_8, u_2) → E_8Translate(D_8, u_2) → F_8Segment(E_8, F_8) → t_3Translate(E_8, u_2) → G_8Translate(F_8, u_2) → H_8Segment(G_8, H_8) → a_3Translate(G_8, u_2) → I_8Translate(H_8, u_2) → J_8Segment(I_8, J_8) → b_3Translate(I_8, u_2) → K_8Translate(J_8, u_2) → L_8Segment(K_8, L_8) → d_3Vector(B_8, I'_4) → v_2Translate(K_8, v_2) → M_8Translate(L_8, v_2) → N_8Segment(M_8, N_8) → e_3Translate(M_8, u_2) → O_8Translate(N_8, u_2) → P_8Segment(O_8, P_8) → f_4Translate(O_8, u_2) → Q_8Translate(P_8, u_2) → R_8Segment(Q_8, R_8) → g_4Translate(Q_8, u_2) → S_8Translate(R_8, u_2) → T_8Segment(S_8, T_8) → h_4Intersect(i_2, ขอบ2) → U_8Vector(C, U_8) → u_3Translate(K, u_3) → K'_3Translate(P, u_3) → P'Translate(K'_3, u_3) → V_8Translate(P', u_3) → P''Translate(V_8, u_3) → W_8Translate(P'', u_3) → P'''Translate(W_8, u_3) → Z_8Translate(P''', u_3) → A_9Translate(Z_8, u_3) → B_9Translate(A_9, u_3) → C_9Translate(B_9, u_3) → D_9Translate(C_9, u_3) → E_9Translate(D_9, u_3) → F_9Translate(E_9, u_3) → G_9Translate(F_9, u_3) → H_9Translate(G_9, u_3) → I_9Translate(H_9, u_3) → J_9Translate(I_9, u_3) → K_9Circle(A, 1, ขอบ1) → c_4Intersect(ขอบ4, c_4) → L_9, M_9Vector(A, M_9) → u_4Translate(I, u_4) → I'_5Translate(T, u_4) → T'Segment(I'_5, T') → ขอบ16'Translate(I'_5, u_4) → N_9Translate(T', u_4) → T''Segment(N_9, T'') → ขอบ16''Translate(N_9, u_4) → O_9Translate(T'', u_4) → T'''Segment(O_9, T''') → ขอบ16'''Translate(O_9, u_4) → P_9Translate(T''', u_4) → Q_9Segment(P_9, Q_9) → p_4Translate(P_9, u_4) → R_9Translate(Q_9, u_4) → S_9Segment(R_9, S_9) → q_4Translate(R_9, u_4) → T_9Translate(S_9, u_4) → U_9Segment(T_9, U_9) → r_4Translate(T_9, u_4) → V_9Translate(U_9, u_4) → W_9Segment(V_9, W_9) → s_4Translate(V_9, u_4) → Z_9Translate(W_9, u_4) → A_{10}Segment(Z_9, A_{10}) → t_4Translate(Z_9, u_4) → B_{10}Translate(A_{10}, u_4) → C_{10}Segment(B_{10}, C_{10}) → a_4Translate(O, v_1) → O'Translate(J, v_1) → J'_3Segment(O', J'_3) → ขอบ8'Translate(O', v_1) → O''Translate(J'_3, v_1) → D_{10}Segment(O'', D_{10}) → ขอบ8''Translate(O'', v_1) → O'''Translate(D_{10}, v_1) → E_{10}Segment(O''', E_{10}) → ขอบ8'''Translate(O''', v_1) → F_{10}Translate(E_{10}, v_1) → G_{10}Segment(F_{10}, G_{10}) → i_4Translate(F_{10}, v_1) → H_{10}Translate(G_{10}, v_1) → I_{10}Segment(H_{10}, I_{10}) → j_4Translate(H_{10}, v_1) → J_{10}Translate(I_{10}, v_1) → K_{10}Segment(J_{10}, K_{10}) → k_4Translate(J_{10}, v_1) → L_{10}Translate(K_{10}, v_1) → M_{10}Segment(L_{10}, M_{10}) → l_4Translate(L_{10}, v_1) → N_{10}Translate(M_{10}, v_1) → O_{10}Segment(N_{10}, O_{10}) → m_4Translate(N_{10}, v_1) → P_{10}Translate(O_{10}, v_1) → Q_{10}Segment(P_{10}, Q_{10}) → n_4