积极 AI Logo 积极 AI

为 Marcela UFTM 创建的立方体模型

为 Marcela UFTM 创建的立方体模型
几何画板及绘图内容加载中，请稍等……
2019-05-11 23:42
向量解析几何立体几何几何作图
所属专题 Developing games and puzzles with 3D printing for STEAM Developing fun games and puzzles with 3D printing for STEAM From POST-IT to 3D PRINTING: playing with squares and cubes
①本范例演示了一个三维立方体的构建与可视化；②涉及的核心数学概念包括直线、概率、质心、旋转和平面；③作图要点——使用了 Point, Polygon, Segment, Midpoint, Centroid, Circle, Intersect, Vector, Translate, Prism 等GeoGebra命令和对象；④适合大学数学基础课程或立体几何教学。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  5. Segment(H, F) → n
  6. Segment(E, G) → p
  7. Midpoint(i) → I
  8. Midpoint(m) → J
  9. Midpoint(l) → K
  10. Midpoint(k) → L
  11. Midpoint(j) → M
  12. Midpoint(n) → N
  13. Midpoint(h) → O
  14. Midpoint(g) → P
  15. Centroid(poly1) → Q
  16. Centroid(poly1) → R
  17. Midpoint(f) → S
  18. Polygon(D, I, J, E, N, H, K, O) → poly3, d, i_1, j_1, e, n_1, h_1, k_1, o
  19. Polygon(O, K, H, N, G, L, P, C) → poly4, o_1, k_2, h_2, n_2, g_1, l_1, p_1, c
  20. Polygon(L, G, N, F, M, S, B, P) → poly5, l_2, g_2, n_3, f_1, m_1, s, b, p_2
  21. Polygon(I, A, S, M, F, N, E, J) → poly6, i_2, a, s_1, m_2, f_2, n_4, e_1, j_2
  22. Circle(N, r) → q
  23. Intersect(q, h_2) → T,
  24. Intersect(q, g_2) → U,
  25. Vector(N, T) → u
  26. Vector(N, U) → v
  27. Translate(O, v) → O'
  28. Translate(K, v) → K'
  29. Translate(H, v) → H'
  30. Translate(N, v) → N'
  31. Translate(G, v) → G'
  32. Translate(L, v) → L'
  33. Translate(P, v) → P'
  34. Translate(C, v) → C'
  35. Polygon(O', K', H', N', G', L', P', C') → poly4', o', k', h', n', g', l', p', c'
  36. Translate(D, u) → D'
  37. Translate(I, u) → I'
  38. Translate(J, u) → J'
  39. Translate(E, u) → E'
  40. Translate(N, u) → N'_1
  41. Translate(H, u) → H'_1
  42. Translate(K, u) → K'_1
  43. Translate(O, u) → O'_1
  44. Polygon(D', I', J', E', N'_1, H'_1, K'_1, O'_1) → poly3', d', i', j', e', n'_1, h'_1, k'_1, o'_1
  45. Translate(I, Vector[(-v)]) → I'_1
  46. Translate(A, Vector[(-v)]) → A'
  47. Translate(S, Vector[(-v)]) → S'
  48. Translate(M, Vector[(-v)]) → M'
  49. Translate(F, Vector[(-v)]) → F'
  50. Translate(N, Vector[(-v)]) → N'_2
  51. Translate(E, Vector[(-v)]) → E'_1
  52. Translate(J, Vector[(-v)]) → J'_1
  53. Polygon(I'_1, A', S', M', F', N'_2, E'_1, J'_1) → poly6', i'_1, a', s', m', f', n'_2, e'_1, j'_1
  54. Translate(L, Vector[(-u)]) → L'_1
  55. Translate(G, Vector[(-u)]) → G'_1
  56. Translate(N, Vector[(-u)]) → N'_3
  57. Translate(F, Vector[(-u)]) → F'_1
  58. Translate(M, Vector[(-u)]) → M'_1
  59. Translate(S, Vector[(-u)]) → S'_1
  60. Translate(B, Vector[(-u)]) → B'
  61. Translate(P, Vector[(-u)]) → P'_1
  62. Polygon(L'_1, G'_1, N'_3, F'_1, M'_1, S'_1, B', P'_1) → poly5', l'_1, g'_1, n'_3, f'_1, m'_1, s'_1, b', p'_1
  63. Prism(poly3', a_1) → b_1, F_1, face10, face11, face12, face13, face14, face15, face9, face16, edge12, edge13, G_1, edge14, edge15, edge16, edge17, edge18, edge19, edge20, edge22, edge23, edge24, H_1, edge25, edge26, edge27, edge21, I_1, J_1, K_1, L_1, M_1, face8
  64. Prism(poly4', q_1) → r_1, V_1, face28, face29, face30, face31, face32, face33, face27, face34, edge28, edge45, W_1, edge46, edge47, edge48, edge49, edge50, edge51, edge52, edge54, edge55, edge56, Z_1, edge57, edge58, edge59, edge53, A_2, B_2, C_2, D_2, E_2, face17
  65. Prism(poly6', d_1) → t_1, N_1, face21, face22, face23, face24, face25, face26, face20, face35, edge30, edge31, O_1, edge32, edge33, edge34, edge35, edge36, edge37, edge38, edge40, edge41, edge42, P_1, edge43, edge44, edge60, edge39, Q_1, R_1, S_1, T_1, U_1, face19
  66. Prism(poly5', u_1) → v_1, F_2, face39, face40, face41, face42, face43, face44, face38, face45, edge63, edge64, G_2, edge65, edge66, edge67, edge68, edge69, edge70, edge71, edge73, edge74, edge75, H_2, edge76, edge77, edge78, edge72, I_2, J_2, K_2, L_2, M_2, face37

AI 绘图提示语参考

绘制一个立方体模型，包含六个面、十二条边和八个顶点。首先在x轴和y轴上各取一个点，然后利用这些点构造两个正方形，接着通过中点和重心等构造其他面。最后通过平移和旋转操作，生成立方体的六个面。
以上提示语为根据原始绘图命令整理而来，仅供参考。