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Build the net of a pyramid by Ivan De Winne

Build the net of a pyramid by Ivan De Winne
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2017-02-20 01:54
PolygonVectorSolid Geometry
This example demonstrates how to construct the net of a pyramid by dragging red and blue faces onto a grey base net. It involves core math concepts like polygons, solid geometry, and vectors. Construction uses commands such as Polygon, Point, Midpoint, Intersect, Pyramid, Net, and Vector. Suitable for high school students learning solid geometry.

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