三维图形旋转与构造
几何画板及绘图内容加载中,请稍等……
①本范例演示了三维图形(如多边形)的旋转构造及其动态变化;②涉及核心数学概念包括立体几何、旋转变换、多边形构造及优化问题;③作图要点运用了Polygon(多边形)、Segment(线段)、Rotate(旋转)等GeoGebra命令与对象;④适合高中及以上学段学习立体几何、几何作图及变换应用。
GeoGebra 命令及参数
Polygon(A, B, 3) → poly1, a, b, c, CSegment(B, D) → dSegment(D, E) → eSegment(E, F) → fSegment(F, G) → gSegment(G, H) → hSegment(H, I) → iSegment(I, J) → jSegment(J, K) → kSegment(K, L) → lSegment(L, M) → mSegment(M, N) → nSegment(N, O) → pSegment(O, P) → qSegment(P, Q) → rSegment(Q, R) → sSegment(R, S) → tSegment(S, T) → a_1Segment(T, U) → b_1Segment(U, V) → c_1Segment(V, W) → d_1Segment(W, Z) → e_1Segment(Z, A_1) → f_1Segment(A_1, B_1) → g_1Segment(B_1, C) → h_1Rotate(B, 60*°, B) → B'Rotate(D, 60*°, B) → D'Segment(B', D') → d'Rotate(D, 60*°, B) → D'_1Rotate(E, 60*°, B) → E'Segment(D'_1, E') → e'Rotate(E, 60*°, B) → E'_1Rotate(F, 60*°, B) → F'Segment(E'_1, F') → f'Rotate(F, 60*°, B) → F'_1Rotate(G, 60*°, B) → G'Segment(F'_1, G') → g'Rotate(G, 60*°, B) → G'_1Rotate(H, 60*°, B) → H'Segment(G'_1, H') → h'Rotate(H, 60*°, B) → H'_1Rotate(I, 60*°, B) → I'Segment(H'_1, I') → i'Rotate(I, 60*°, B) → I'_1Rotate(J, 60*°, B) → J'Segment(I'_1, J') → j'Rotate(J, 60*°, B) → J'_1Rotate(K, 60*°, B) → K'Segment(J'_1, K') → k'Rotate(K, 60*°, B) → K'_1Rotate(L, 60*°, B) → L'Segment(K'_1, L') → l'Rotate(L, 60*°, B) → L'_1Rotate(M, 60*°, B) → M'Segment(L'_1, M') → m'Rotate(M, 60*°, B) → M'_1Rotate(N, 60*°, B) → N'Segment(M'_1, N') → n'Rotate(N, 60*°, B) → N'_1Rotate(O, 60*°, B) → O'Segment(N'_1, O') → p'Rotate(O, 60*°, B) → O'_1Rotate(P, 60*°, B) → P'Segment(O'_1, P') → q'Rotate(P, 60*°, B) → P'_1Rotate(Q, 60*°, B) → Q'Segment(P'_1, Q') → r'Rotate(Q, 60*°, B) → Q'_1Rotate(R, 60*°, B) → R'Segment(Q'_1, R') → s'Rotate(R, 60*°, B) → R'_1Rotate(S, 60*°, B) → S'Segment(R'_1, S') → t'Rotate(S, 60*°, B) → S'_1Rotate(T, 60*°, B) → T'Segment(S'_1, T') → i_1Rotate(T, 60*°, B) → T'_1Rotate(U, 60*°, B) → U'Segment(T'_1, U') → j_1Rotate(U, 60*°, B) → U'_1Rotate(V, 60*°, B) → V'Segment(U'_1, V') → k_1Rotate(V, 60*°, B) → V'_1Rotate(W, 60*°, B) → W'Segment(V'_1, W') → l_1Rotate(W, 60*°, B) → W'_1Rotate(Z, 60*°, B) → Z'Segment(W'_1, Z') → m_1Rotate(Z, 60*°, B) → Z'_1Rotate(A_1, 60*°, B) → C_1Segment(Z'_1, C_1) → n_1Rotate(A_1, 60*°, B) → D_1Rotate(B_1, 60*°, B) → E_1Segment(D_1, E_1) → p_1Rotate(B_1, 60*°, B) → F_1Rotate(C, 60*°, B) → C'Segment(F_1, C') → q_1Rotate(B', 60*°, A) → B''Rotate(D', 60*°, A) → D''Segment(B'', D'') → d''Rotate(D'_1, 60*°, A) → G_1Rotate(E', 60*°, A) → E''Segment(G_1, E'') → e''Rotate(E'_1, 60*°, A) → H_1Rotate(F', 60*°, A) → F''Segment(H_1, F'') → f''Rotate(F'_1, 60*°, A) → I_1Rotate(G', 60*°, A) → G''Segment(I_1, G'') → g''Rotate(G'_1, 60*°, A) → J_1Rotate(H', 60*°, A) → H''Segment(J_1, H'') → h''Rotate(H'_1, 60*°, A) → K_1Rotate(I', 60*°, A) → I''Segment(K_1, I'') → i''Rotate(I'_1, 60*°, A) → L_1Rotate(J', 60*°, A) → J''Segment(L_1, J'') → j''Rotate(J'_1, 60*°, A) → M_1Rotate(K', 60*°, A) → K''Segment(M_1, K'') → k''Rotate(K'_1, 60*°, A) → N_1Rotate(L', 60*°, A) → L''Segment(N_1, L'') → l''Rotate(L'_1, 60*°, A) → O_1Rotate(M', 60*°, A) → M''Segment(O_1, M'') → m''Rotate(M'_1, 60*°, A) → P_1Rotate(N', 60*°, A) → N''Segment(P_1, N'') → n''Rotate(N'_1, 60*°, A) → Q_1Rotate(O', 60*°, A) → O''Segment(Q_1, O'') → p''Rotate(O'_1, 60*°, A) → R_1Rotate(P', 60*°, A) → P''Segment(R_1, P'') → q''Rotate(P'_1, 60*°, A) → S_1Rotate(Q', 60*°, A) → Q''Segment(S_1, Q'') → r''Rotate(Q'_1, 60*°, A) → T_1Rotate(R', 60*°, A) → R''Segment(T_1, R'') → s''Rotate(R'_1, 60*°, A) → U_1Rotate(S', 60*°, A) → S''Segment(U_1, S'') → t''Rotate(S'_1, 60*°, A) → V_1Rotate(T', 60*°, A) → T''Segment(V_1, T'') → r_1Rotate(T'_1, 60*°, A) → W_1Rotate(U', 60*°, A) → U''Segment(W_1, U'') → s_1Rotate(U'_1, 60*°, A) → Z_1Rotate(V', 60*°, A) → V''Segment(Z_1, V'') → t_1Rotate(V'_1, 60*°, A) → A_2Rotate(W', 60*°, A) → W''Segment(A_2, W'') → a_2Rotate(W'_1, 60*°, A) → B_2Rotate(Z', 60*°, A) → Z''Segment(B_2, Z'') → b_2Rotate(Z'_1, 60*°, A) → C_2Rotate(C_1, 60*°, A) → D_2Segment(C_2, D_2) → c_2Rotate(D_1, 60*°, A) → E_2Rotate(E_1, 60*°, A) → F_2Segment(E_2, F_2) → d_2Rotate(F_1, 60*°, A) → G_2Rotate(C', 60*°, A) → C''Segment(G_2, C'') → e_2Rotate(B, 60*°, A) → B'_1Polygon(B, D', M', M'_1, O', P', Q', R', S', T', U', V', E', W', Z', C_1, E_1, A, F_2, D_2, Z'', W'', V'', F', U'', T'', S'', R'', Q'', P'', O'', N'', M'', L'', G', K'', J'', I'', H'', G'', E'', H_1, D'', C, B_1, H', A_1, Z, W, V, U, T, S, R, Q, P, I', O, N, M, L, K, J, I, H, G, F, J', E, D, K', L') → poly2, b_3, l'_1, m'_1, m'_2, o', p'_1, q'_1, r'_1, s'_1, t'_1, u', d'_1, v', w', z', c_3, e_3, a_3, f_2, d_3, z'', w'', e'_1, v'', u'', t''_1, s''_1, r''_1, q''_1, p''_1, o'', n''_1, m''_1, f'_1, l''_1, k''_1, j''_1, i''_1, h''_1, g''_1, e''_1, h_2, d''_1, c_4, g'_1, b_4, a_4, z, w, v, u, t_2, s_2, r_2, q_2, h'_1, p_2, o, n_2, m_2, l_2, k_2, j_2, i_2, h_3, g_2, i'_1, f_3, e_4, d_4, j'_1, k'_1
AI 绘图提示语参考
画一个由多个线段组成的闭合多边形,然后以多边形的一个顶点为旋转中心,将多边形整体旋转60度,依次画出旋转后每个顶点的位置,并连接相邻旋转后的顶点形成新的多边形,展示旋转构造的过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。