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2020-02-06 18:03

多边形立体几何

所属专题 Developing fun games and puzzles with 3D printing for STEAM

①本范例演示了多边形的边与顶点关系，通过构造和变换展示几何图形的动态变化；②涉及的核心数学概念包括多边形构造、平移变换、圆与三角形的关系、正交中心等；③作图要点提炼自构造摘要，使用了Polygon（多边形）、Prism（棱柱）、点T, K_3, J_3, K_2, G_3, F_3, E_3, D_3, B_3, A_3, F_2, E_2, D_2, C_2, B_2, A_2, Z_1, W_1, V_1, O_1, N_1, I_1, H_1, G_1, F_1, E_1, E, F, G, H, J, K, L, M, N, O, Q, R, S, U等对象及命令；④适合高中及以上学段学习立体几何、解析几何及几何变换，可用于教学演示和探究活动。

GeoGebra 命令及参数

Polygon(A, B, C, D) → poly1, f, g, h, i
Polygon(J_1, Q, W_2, Z_2, M, N, O, D_3, E_3, F_3, G_3, N_1, R, L, G_2, Q_2, R_2, S_2, T_2, U_2, H_2, I_2, J_2, T, K_2, L_2, M_2, D_2, N_2, E_2, F_2, O_2, P_2, W_1, P, J_3, K_3, V_1, Z_1, B_2, A_2, C_2, O_1, I_1, H_1, S, G_1, F_1, E_1, D_1, I_3, K, J, H, G, F, B_3, E, C_1, B_1, A_1, Z, W, V, U, A_3, H_3, V_2) → poly2, j, t, a, b, c, d, e, f_1, g_1, h_1, i_1, k, j_1, k_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, t_1, l, a_1, b_1, c_1, d_1, e_1, f_2, g_2, h_2, i_2, j_2, m, k_2, l_2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, a_2, n, b_2, c_2, d_2, e_2, f_3, g_3, h_3, i_3, j_3, k_3, p, l_3, m_3, n_3, p_3, q_3, r_3, s_3, t_3, a_3, q, r, s
Prism(poly2, u) → v, V_5, G_6, face128, face88, face89, face87, face85, face86, face129, face95, face74, face72, H_6, face73, face94, face93, face92, face90, face91, face96, face98, face99, face100, I_6, face101, face102, face124, face109, face108, face107, face106, face105, face103, face104, J_6, face123, face122, face121, face120, face119, face117, face118, face138, edge184, edge173, K_6, edge174, edge137, edge204, edge175, edge145, edge146, edge202, edge199, edge200, edge201, L_6, edge170, edge171, edge172, edge144, edge143, edge142, edge141, edge157, edge169, edge193, M_6, edge194, edge195, edge196, edge197, edge198, edge185, edge186, edge187, edge140, edge188, N_6, edge189, edge149, edge190, edge148, edge147, edge191, edge192, edge154, edge139, edge138, O_6, edge155, edge153, edge151, edge152, edge150, edge156, edge158, edge159, edge160, edge161, P_6, edge162, edge183, edge203, edge168, edge167, edge166, edge165, edge164, edge163, edge182, W_5, Q_6, edge181, edge180, edge179, edge178, edge177, edge176, edge205, edge207, edge208, edge209, R_6, edge210, edge211, edge212, edge213, edge214, edge215, edge216, edge217, edge218, edge219, S_6, edge220, edge221, edge222, edge223, edge224, edge225, edge226, edge227, edge228, edge229, T_6, edge230, edge231, edge232, edge233, edge234, edge235, edge236, edge237, edge238, edge239, U_6, edge240, edge241, edge242, edge243, edge244, edge245, edge246, edge247, edge248, edge249, V_6, edge250, edge251, edge252, edge253, edge254, edge255, edge256, edge257, edge258, edge259, W_6, edge260, edge261, edge262, edge263, edge264, edge265, edge266, edge267, edge268, edge269, Z_6, edge270, edge271, edge272, edge206, A_7, B_7, Z_5, C_7, D_7, E_7, F_7, G_7, H_7, I_7, J_7, K_7, L_7, A_6, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7, B_6, W_7, Z_7, A_8, B_8, C_8, D_8, E_8, F_8, G_8, H_8, C_6, I_8, J_8, K_8, L_8, M_8, N_8, O_8, P_8, Q_8, face115, D_6, face114, face70, face71, face116, face83, face82, face84, face136, face135, face137, E_6, face112, face111, face113, face81, face80, face79, face77, face78, face97, face110, F_6, face130, face131, face132, face133, face134, face126, face125, face127, face75, face76
Polygon(K_1, P_1, M_1, L_1) → q1, b_3, c_3, d_3, e_3
Prism(q1, w) → o_1, U_1, edge9, edge12, edge11, edge10, edge13, edge15, edge16, edge14, C_3, L_3, M_3, face7, face9, face8, face6, face10

AI 绘图提示语参考

画一个多边形，然后基于这个多边形创建一个棱柱，接着用四个点再画一个小的多边形，最后基于这个小多边形创建另一个棱柱，展示多边形、棱柱以及它们之间的动态关系。

以上提示语为根据原始绘图命令整理而来，仅供参考。