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Build the net of a pyramid

Build the net of a pyramid
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2018-07-01 10:16
PolygonSolid GeometryGeometric Construction
This example demonstrates how to construct the net of a pyramid by dragging red and blue faces onto the grey net. It involves core math concepts like polygons, solid geometry, and geometric construction. Construction highlights include using commands/objects such as Polygon, Point, Midpoint, Intersect, Pyramid, Net. Suitable for high school students learning solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(M, N, C_1) → poly3, n, q, r
  2. Point(Circle[K_5, 1]) → L_5
  3. Polygon(K_5, L_5, M_5) → Vieleck1, m_5, k_5, l_5
  4. Point(Circle[N_5, 1]) → O_5
  5. Polygon(N_5, O_5, P_5) → Vieleck2, p_5, n_5, o_5
  6. Point(Circle[Q_5, 1]) → R_5
  7. Polygon(Q_5, R_5, S_5) → Vieleck3, s_5, q_5, r_5
  8. Point(Circle[T_5, 1]) → U_5
  9. Polygon(T_5, U_5, V_5) → Vieleck4, v_5, t_5, u_5
  10. Point(Circle[V_4, 2]) → W_4
  11. Midpoint(A_5, V_4) → J_5
  12. Point(Circle[F_4, 2]) → G_4
  13. Midpoint(I_4, F_4) → I_5
  14. Point(Circle[J_4, 2]) → K_4
  15. Midpoint(U_4, J_4) → H_5
  16. Midpoint(Z_4, W_4) → G_5
  17. Midpoint(H_4, G_4) → F_5
  18. Point(Circle[B_4, 2]) → C_4
  19. Midpoint(B_4, E_4) → E_5
  20. Midpoint(T_4, K_4) → D_5
  21. Intersect(zAxis, xAxis) → A
  22. Point(xAxis) → B
  23. Polygon(A, B, 4, xOyPlane) → poly1, f, g, h, i, C, D
  24. Pyramid(poly1, 2) → a, E, Fläche1, Fläche2, Fläche3, Fläche4, Kante1, Kante2, Kante3, Kante4
  25. Point(Circle[B, Distance[A, B], Segment[A, B]]) → I
  26. Net(a, c) → d, V_1, G_2, H_2, I_2, J_2, K_2, face1, face2, face4, face5, face3, W_1, face6, edge1, edge5, edge8, edge2, edge3, edge13, edge6, edge7, edge16, Z_1, edge9, edge10, edge17, edge11, edge12, edge18, edge4, edge15, A_2, B_2, C_2, D_2, E_2, F_2
  27. Net(a, o) → p, H_3, Q_3, R_3, S_3, T_3, U_3, face13, face14, face16, face17, face15, I_3, face18, edge39, edge43, edge46, edge40, edge41, edge51, edge44, edge45, edge54, J_3, edge47, edge48, edge55, edge49, edge50, edge56, edge42, edge53, K_3, L_3, M_3, N_3, O_3, P_3
  28. Polygon(Z_2, A_3, 4) → poly7, m_1, n_1, p_1, q_1, B_3, C_3
  29. Polygon(C_4, D_4, E_5) → poly9, j_1, k_1, l_1
  30. Polygon(G_4, H_4, I_5) → poly10, b_1, c_1, d_1
  31. Polygon(V_3, W_3, 4) → poly8, r_1, s_1, t_1, a_1, Z_3, A_4
  32. Polygon(W_4, Z_4, J_5) → poly12, e_1, f_2, g_2
  33. Polygon(K_4, T_4, H_5) → poly11, m, h_1, i_1
  34. Polygon(K, L, M) → poly2, j, k, l
  35. Polygon(L, O_2, Q_2) → poly4, e, f_1, g_1
  36. Polygon(N, O_2, R_2) → poly5, s, t, b
  37. Polygon(L, O_2, N, M) → poly6, l_2, o_3, n_4, m_3
  38. Polygon(T_2, U_2, P_2, Q_2) → poly13, t_2, u_2, p_3, q_3
  39. AreEqual(poly7, poly8) → CheckSquares
  40. AreEqual(poly6, poly7) → check5
  41. Vector(B_5, C_5) → u
  42. Vector(F, G) → v

AI Drawing Prompt Reference

Draw the net of a square pyramid. Start with a square base and a vertex above its center to form the pyramid. Then unfold the pyramid into a flat net consisting of four triangular faces and one square base, all connected along shared edges. Around the net, place several draggable colored triangular and square faces that match the shapes of the net's faces, for assembly practice. Also include some auxiliary circles and points near the net to help position these faces. The scene illustrates the transformation from a 3D pyramid to its 2D net, suitable for geometry construction exercises.
The prompt above was compiled from the original drawing commands and is for reference only.