可调节棱柱：动态几何演示与展开图

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2017-11-24 01:15

本范例通过GeoGebra动态展示了一个可调节的棱柱，包括其三维立体结构、侧面展开图以及相关几何参数的变化。核心数学概念涉及立体几何中的棱柱、棱锥、多边形、对称变换以及分数比例关系。作图要点包括使用Mirror命令创建对称对象，Polygon和Prism命令构建棱柱主体，Net命令生成展开图，Pyramid命令辅助构造锥体；对象涵盖多个顶点（A, B, C, D等）、面（faceAA'MN, faceABON等）以及高度变量Height。该范例适合中学数学立体几何教学，帮助学生直观理解棱柱的构成、展开图与空间想象，也可用于探究棱柱体积、表面积与参数变化的关系。

GeoGebra 命令及参数

Mirror(A, yAxis) → A'
Polygon(A', A, Sides) → poly1, f, q, B, C, D, E_1, F, G, H, I, g, h, i, j, k, l, m, p
Prism(poly1, Height) → b, M, F_2, faceAA'MN, faceABON, faceA'BOM, face1, face3, face5, face7, face9, face11, N, face13, faceMNO, edgeA'M, edgeAN, edgeBO, edge1, edge8, edge15, edge22, edge29, O, edge36, edge43, edgeMN, edgeNO, edgeMO, edge2, edge9, edge16, edge23, edge30, W, edge37, edge44, D_1, J_1, O_1, T_1, A_2
Net(b, Open) → c, J, G_2, P, Q, R, S, T, U, B_1, C_1, H_1, K, I_1, M_1, N_1, R_1, S_1, W_1, Z_1, D_2, E_2, I_2, L, J_2, V, A_1, G_1, L_1, Q_1, V_1, C_2, H_2, faceJKL, Z, faceJKQP, faceKLSR, faceJLTU, face2, face4, face6, face8, face10, face12, face14, F_1, facePQV, edgeJK, edgeKL, edgeJL, edge4, edge11, edge18, edge25, edge32, edge39, K_1, edge46, edgeJP, edgePQ, edgeKQ, edgeKR, edgeRS, edgeLS, edgeLT, edgeTU, edgeJU, P_1, edge5, edge6, edge7, edge12, edge13, edge14, edge19, edge20, edge21, edge26, U_1, edge27, edge28, edge33, edge34, edge35, edge40, edge41, edge42, edge47, edge48, B_2, edge49, edgeQV, edgePV, edge3, edge10, edge17, edge24, edge31, edge38, edge45
Polygon(A', A, Sides) → poly2, r, i_1, E, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, s, t, a, d, e, f_1, g_1, h_1
Pyramid(poly2, Height) → u, S_2, face34, face27, edge61, edge60, edge62, edge63, edge64, edge65, edge66, edge67, face25, edge68, edge69, face26, face28, face29, face30, face31, face32, face33
Net(u, Open2) → v, R_2, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, T_2, N_3, face35, face15, face17, face18, face19, face20, face21, face22, face23, U_2, face24, face16, edge50, edge54, edge57, edge70, edge73, edge76, edge79, edge82, V_2, edge85, edge51, edge52, edge55, edge56, edge58, edge59, edge71, edge72, edge74, W_2, edge75, edge77, edge78, edge80, edge81, edge83, edge84, edge86, edge87, edge88, Z_2, edge89, edge53, A_3, B_3, C_3