正多边形底面的棱锥展开图

正多边形底面的棱锥展开图
几何画板及绘图内容加载中,请稍等……
2023-04-07 20:01
这个范例演示了正多边形底面的棱锥展开图。涉及的核心数学概念包括立体几何和几何作图。通过使用CurveCartesian, Point, Polygon, Pyramid, Net等GeoGebra命令,可以构造出棱锥的展开图。适合高中阶段的学生和教师使用。

GeoGebra 命令及参数

  1. CurveCartesian((4 * sin(t)), (4 * cos(t)), 0, t, 0, 6.28319) → a
  2. Point(a) → B
  3. Polygon(B, A, Faces, xOyPlane) → poly1, c, r, C_{11}, D_{11}, E_{11}, F_{11}, W_{16}, H_{17}, Q_{17}, R_{17}, S_{17}, T_{17}, s, U_{17}, V_{17}, W_{17}, Z_{17}, A_{18}, B_{18}, C_{18}, D_{18}, E_{18}, t, a_1, b_1, c_1, d_1, e_1, f_1, g_1, d, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1, q_1, r_1, e, s_1, t_1, a_2, b_2, c_2, d_2, e_2, f_2, g_2, h_2, k, i_2, j_2, k_2, l_2, m_2, n_2, p_2, q_2, r_2, s_2, l, t_2, a_3, b_3, c_3, d_3, e_3, f_3, g_3, h_3, i_3, m, j_3, C, E_1, F_1, W_1, Z_1, A_2, B_2, C_2, D_2, n, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, E_7, F_7, p, G_7, H_7, I_7, J_7, K_7, L_7, M_7, N_{10}, O_{10}, P_{10}, q, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}
  4. Pyramid(poly1, 4) → f, D, face18, edge344, edge345, edge346, edge347, edge348, edge349, edge350, edge555, edge568, edge581, face19, edge582, edge583, edge584, edge585, edge586, edge587, edge588, edge589, edge590, edge591, face20, edge592, edge593, face21, face22, face23, face24, face25, face26, face27, faceABD, face28, face85, face86, face87, face88, face89, face90, face91, face92, face93, faceACD, face130, face131, face132, face133, face134, face135, face136, face137, face138, face139, faceBCD, face140, face141, face142, face143, face144, face145, face146, face215, face220, face225, face5, face226, face227, face228, face229, face230, face231, face232, face233, face234, face235, face6, face236, face237, edgeBD, edgeAD, edgeCD, edge9, edge10, edge35, edge36, edge37, face15, edge38, edge39, edge40, edge41, edge42, edge43, edge44, edge45, edge46, edge47, face16, edge48, edge217, edge218, edge219, edge220, edge221, edge222, edge223, edge224, edge225, face17, edge334, edge335, edge336, edge337, edge338, edge339, edge340, edge341, edge342, edge343
  5. Net(f, g) → b, Q, A_5, G_{15}, H_{15}, I_{15}, J_{15}, K_{15}, L_{15}, E_{17}, N_{17}, W_{20}, Z_{20}, B_5, A_{21}, B_{21}, C_{21}, D_{21}, E_{21}, F_{21}, G_{21}, H_{21}, I_{21}, J_{21}, C_5, K_{21}, faceQRS, faceQRT, faceRSU, faceQSV, face11, face12, face57, face58, face59, D_5, face60, face61, face62, face63, face64, face65, face66, face67, face68, face69, E_5, face70, face112, face113, face114, face115, face116, face117, face118, face119, face120, F_5, face181, face182, face183, face184, face185, face186, face187, face188, face189, face190, G_5, face191, face192, face193, face194, face195, face196, face197, face218, face223, face264, H_5, face265, face266, face267, face268, face269, face270, face271, face272, face273, face274, I_5, face275, face276, edgeQR, edgeRS, edgeQS, edge23, edge24, edge133, edge134, edge135, J_5, edge136, edge137, edge138, edge139, edge140, edge141, edge142, edge143, edge144, edge145, R, B_9, edge146, edge280, edge281, edge282, edge283, edge284, edge285, edge286, edge287, edge288, C_9, edge453, edge454, edge455, edge456, edge457, edge458, edge459, edge460, edge461, edge462, D_9, edge463, edge464, edge465, edge466, edge467, edge468, edge469, edge562, edge575, edge672, E_9, edge673, edge674, edge675, edge676, edge677, edge678, edge679, edge680, edge681, edge682, F_9, edge683, edge684, edgeQT, edgeRT, edgeRU, edgeSU, edgeSV, edgeQV, edge25, edge26, G_9, edge27, edge28, edge147, edge148, edge149, edge150, edge151, edge152, edge153, edge154, H_9, edge155, edge156, edge157, edge158, edge159, edge160, edge161, edge162, edge163, edge164, I_9, edge165, edge166, edge167, edge168, edge169, edge170, edge171, edge172, edge173, edge174, J_9, edge289, edge290, edge291, edge292, edge293, edge294, edge295, edge296, edge297, edge298, C_{14}, edge299, edge300, edge301, edge302, edge303, edge304, edge305, edge306, edge470, edge471, S, D_{14}, edge472, edge473, edge474, edge475, edge476, edge477, edge478, edge479, edge480, edge481, E_{14}, edge482, edge483, edge484, edge485, edge486, edge487, edge488, edge489, edge490, edge491, F_{14}, edge492, edge493, edge494, edge495, edge496, edge497, edge498, edge499, edge500, edge501, G_{14}, edge502, edge503, edge563, edge564, edge576, edge577, edge685, edge686, edge687, edge688, H_{14}, edge689, edge690, edge691, edge692, edge693, edge694, edge695, edge696, edge697, edge698, I_{14}, edge699, edge700, edge701, edge702, edge703, edge704, edge705, edge706, edge707, edge708, J_{14}, edge709, edge710, K_{14}, L_{14}, M_{14}, O_1, N_{14}, O_{14}, P_{14}, Q_{14}, R_{14}, S_{14}, D_{17}, M_{17}, J_{20}, K_{20}, P_1, L_{20}, M_{20}, N_{20}, O_{20}, P_{20}, Q_{20}, R_{20}, S_{20}, T_{20}, U_{20}, U_4, V_{20}, T, U, V, Q_1, R_1, K_5, L_5, M_5, N_5, V_4, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5, W_4, K_9, L_9, M_9, N_9, O_9, P_9, Q_9, R_9, S_9, T_{14}, Z_4, U_{14}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}, D_{15}, E_{15}, F_{15}
  6. Net(f, g) → h, E, T_1, face100, face101, face102, face103, face104, face105, face106, face107, face108, face109, N_2, face110, face111, face147, face148, face149, face150, face151, face152, face153, face154, P_2, face155, face156, edgeEF, edgeFG, edgeEG, edge1, edge5, edge8, edge15, edge20, R_2, edge31, edge34, edge51, edge54, edge57, edge60, edge61, edge62, edge69, edge70, T_2, edge75, edge76, edge77, edge78, edge87, edge88, edge89, edge90, edge93, edge94, U_2, edge95, edge110, edge111, edge112, edge113, edge114, edge115, edge116, edge117, edge118, V_2, edge119, edge120, edgeEK, edgeFK, edgeFL, edgeGL, edgeGM, edgeEM, edge2, edge3, B_3, edge6, edge7, edge13, edge14, edge16, edge19, edge21, edge22, edge32, edge33, C_3, edge49, edge50, edge52, edge53, edge55, edge56, edge58, edge59, edge63, edge64, F_3, edge65, edge66, edge67, edge68, edge71, edge72, edge73, edge74, edge79, edge80, F, G_3, edge81, edge82, edge83, edge84, edge85, edge86, edge96, edge97, edge98, edge99, H_3, edge100, edge101, edge102, edge103, edge104, edge105, edge106, edge107, edge108, edge109, I_3, edge121, edge122, edge123, edge124, edge125, edge126, edge127, edge128, edge129, edge130, N_3, edge131, edge132, edge189, edge190, edge191, edge192, edge193, edge194, edge195, edge196, O_3, edge197, edge198, P_3, Q_3, R_3, S_3, T_3, G, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, W, N_4, K, L, M, Z, G_1, I_1, K_1, M_1, S_1, A_1, M_2, O_2, Q_2, S_2, W_2, Z_2, A_3, D_3, E_3, J_3, H_1, K_3, L_3, M_3, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, J_1, O_4, P_4, Q_4, R_4, S_4, T_4, A_6, B_6, C_6, D_6, L_1, E_6, faceEFG, faceEFK, faceFGL, faceEGM, face1, face3, face36, face37, face38, N_1, face39, face40, face41, face42, face94, face95, face96, face97, face98, face99

AI 绘图提示语参考

绘制一个以正多边形为底面的棱锥展开图。先画一个圆,在圆上取一点作为底面多边形的一个顶点,结合水平面构造出正多边形底面。以该底面为基础,向上构建一个棱锥,棱锥的顶点位于底面中心正上方。随后,将棱锥的各个侧面沿底边展开到水平面上,形成展开图,展开后的侧面三角形与底面多边形共边,整体呈现一个平面图形,包含底面多边形和多个三角形面片,展示棱锥的完整表面展开。
以上提示语为根据原始绘图命令整理而来,仅供参考。