Net of a 50-agon Pyramid: Solid Geometry and Centroid Application
Loading the math board and drawing, please wait…
This example demonstrates the construction of a 50-sided pyramid net, focusing on solid geometry concepts, centroid calculations, and polygon unfolding principles. Key construction steps involve using GeoGebra commands like Intersect, Point, Polygon, Pyramid, Centroid, and Net to create polygon vertices, determine pyramid apex positions, calculate centroid coordinates, and generate unfolded surfaces. Suitable for high school students learning solid geometry and centroid applications, or as a mathematical modeling teaching case.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → APoint(xAxis) → BPolygon(A, B, 50) → poly1, a, j, k, l, m, n, p, q, r, s, t, b, a_1, b_1, c_1, d_1, e_1, f_1, g_1, h_1, i_1, j_1, c, k_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, t_1, a_2, d, b_2, c_2, d_2, e_2, f_2, g_2, h_2, i_2, j_2, k_2, e, l_2, C, D, E, F, G, H, I, J, K, f, L, M, N, O, P, Q, R, S, T, U, g, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, h, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, i, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2Pyramid(poly1, 20) → o, D_2, face10, edge49, edge50, face11, face12, face13, face14, face15, face16, face17, face18, face19, face1, face20, face21, face22, face23, face24, face25, face26, face27, face28, face29, face3, face30, face31, face32, face33, face34, face35, face36, face37, face38, face39, face4, face40, face41, face42, face43, face44, face45, face46, face47, face48, face49, face5, face50, face2, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, face6, edge9, edge10, edge11, edge12, edge13, edge14, edge15, edge16, edge17, edge18, face7, edge19, edge20, edge21, edge22, edge23, edge24, edge25, edge26, edge27, edge28, face8, edge29, edge30, edge31, edge32, edge33, edge34, edge35, edge36, edge37, edge38, face9, edge39, edge40, edge41, edge42, edge43, edge44, edge45, edge46, edge47, edge48Centroid(poly1) → C_2Net(o, v) → u, E_2, N_2, H_6, face51, face52, face53, face54, face55, face56, face57, face58, face59, O_2, face60, face61, face62, face63, face64, face65, face66, face67, face68, face69, P_2, face70, face71, face72, face73, face74, face75, face76, face77, face78, face79, Q_2, face80, face81, face82, face83, face84, face85, face86, face87, face88, face89, R_2, face90, face91, face92, face93, face94, face95, face96, face97, face98, face99, S_2, face100, face101, edge51, edge52, edge53, edge54, edge55, edge56, edge57, edge58, T_2, edge59, edge60, edge61, edge62, edge63, edge64, edge65, edge66, edge67, edge68, U_2, edge69, edge70, edge71, edge72, edge73, edge74, edge75, edge76, edge77, edge78, V_2, edge79, edge80, edge81, edge82, edge83, edge84, edge85, edge86, edge87, edge88, W_2, edge89, edge90, edge91, edge92, edge93, edge94, edge95, edge96, edge97, edge98, F_2, Z_2, edge99, edge100, edge101, edge102, edge103, edge104, edge105, edge106, edge107, edge108, A_3, edge109, edge110, edge111, edge112, edge113, edge114, edge115, edge116, edge117, edge118, B_3, edge119, edge120, edge121, edge122, edge123, edge124, edge125, edge126, edge127, edge128, C_3, edge129, edge130, edge131, edge132, edge133, edge134, edge135, edge136, edge137, edge138, D_3, edge139, edge140, edge141, edge142, edge143, edge144, edge145, edge146, edge147, edge148, E_3, edge149, edge150, edge151, edge152, edge153, edge154, edge155, edge156, edge157, edge158, F_3, edge159, edge160, edge161, edge162, edge163, edge164, edge165, edge166, edge167, edge168, G_3, edge169, edge170, edge171, edge172, edge173, edge174, edge175, edge176, edge177, edge178, H_3, edge179, edge180, edge181, edge182, edge183, edge184, edge185, edge186, edge187, edge188, I_3, edge189, edge190, edge191, edge192, edge193, edge194, edge195, edge196, edge197, edge198, G_2, J_3, edge199, edge200, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, R_3, S_3, H_2, T_3, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, I_2, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, J_2, P_4, Q_4, R_4, S_4, T_4, U_4, V_4, W_4, Z_4, A_5, K_2, B_5, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, K_5, L_2, L_5, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, M_2, V_5, W_5, Z_5, A_6, B_6, C_6, D_6, E_6, F_6, G_6
AI Drawing Prompt Reference
Draw the net of a 50-sided pyramid, showcasing solid geometry and centroid applications. Start by plotting the intersection point of the coordinate axes and a point on the x-axis, then create a 50-sided polygon based on these points. Determine the apex of the pyramid above the base and construct the 3D pyramid shape. Calculate the centroid of the base and generate the unfolded net, showing how the pyramid's faces unfold into a flat layout.
The prompt above was compiled from the original drawing commands and is for reference only.