构建金字塔的展开图

构建金字塔的展开图
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2018-07-01 10:16
本范例通过拖动红色和蓝色面到灰色展开图上,演示如何构建金字塔的展开图。涉及的核心数学概念包括多边形、立体几何和几何作图。作图要点:使用了Polygon(多边形)、Point(点)、Midpoint(中点)、Intersect(交点)、Pyramid(金字塔)、Net(展开图)等GeoGebra命令和对象。适合高中阶段学习立体几何和几何作图的学生使用。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个四棱锥的展开图。先构建一个正方形底面,以其中心为顶点向上形成四棱锥。然后生成该棱锥的展开网,包含四个三角形侧面和一个正方形底面,各面通过公共边连接。在展开图周围,放置多个可拖动的彩色三角形和正方形面片,这些面片与展开图的对应面形状相同,用于拼合验证。同时,在展开图附近绘制一些辅助圆和点,用于定位面片的位置。整体呈现一个立体几何构造练习场景,展示棱锥从立体到平面展开的过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。