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有趣立体体的对偶性

有趣立体体的对偶性
几何画板及绘图内容加载中，请稍等……
2019-05-19 18:12
立体几何几何作图函数图像
①本范例演示了不同几何体（如立方体、球体）的对偶关系；②涉及核心数学概念包括立体几何、线性回归、二次方程、切线等；③作图要点使用了Polygon（多边形）、Sphere（球体）、Intersect（相交）、Distance（距离）等GeoGebra命令；④适合高中及以上学生及数学爱好者用于探索空间几何与代数关系。

GeoGebra 命令及参数

  1. Polygon(V0, V6, V22, V30, V18) → A1, v0, v6, v22, v30, v18
  2. Polygon(V0, V18, V16, V34, V8) → A2, f, g, v16, v34, v8
  3. Polygon(V0, V8, V24, V36, V20) → A3, h, i, v24, v36, v20
  4. Polygon(V0, V20, V14, V32, V6) → A4, j, k, v14, v32, l
  5. Polygon(V1, V7, V23, V33, V19) → A5, v1, v7, v23, v33, v19
  6. Polygon(V1, V19, V17, V37, V9) → A6, m, n, v17, v37, v9
  7. Polygon(V1, V9, V25, V35, V21) → A7, p, q, v25, v35, v21
  8. Polygon(V1, V21, V15, V31, V7) → A8, r, s, v15, v31, a
  9. Polygon(V2, V10, V27, V33, V23) → A9, v2, v10, v27, b, c
  10. Polygon(V2, V23, V7, V31, V11) → A10, d, e, f_1, g_1, v11
  11. Polygon(V2, V11, V26, V30, V22) → A11, h_1, i_1, v26, j_1, k_1
  12. Polygon(V2, V22, V6, V32, V10) → A12, l_1, m_1, n_1, p_1, q_1
  13. Polygon(V3, V12, V29, V35, V25) → A13, v3, v12, v29, r_1, s_1
  14. Polygon(V3, V25, V9, V37, V13) → A14, t_1, a_1, b_1, c_1, v13
  15. Polygon(V3, V13, V28, V36, V24) → A15, d_1, e_1, v28, f_2, g_2
  16. Polygon(V3, V24, V8, V34, V12) → A16, h_2, i_2, j_2, k_2, l_2
  17. Polygon(V4, V15, V21, V35, V29) → A17, v4, m_2, n_2, p_2, q_2
  18. Polygon(V4, V29, V12, V34, V16) → A18, r_2, s_2, t_2, a_2, b_2
  19. Polygon(V4, V16, V18, V30, V26) → A19, c_2, d_2, e_2, f_3, g_3
  20. Polygon(V4, V26, V11, V31, V15) → A20, h_3, i_3, j_3, k_3, l_3
  21. Polygon(V5, V14, V20, V36, V28) → A21, v5, m_3, n_3, p_3, q_3
  22. Polygon(V5, V28, V13, V37, V17) → A22, r_3, s_3, t_3, a_3, b_3
  23. Polygon(V5, V17, V19, V33, V27) → A23, c_3, d_3, e_3, f_4, g_4
  24. Polygon(V5, V27, V10, V32, V14) → A24, h_4, i_4, j_4, k_4, l_4
  25. Polygon(W2, W12, W0, W14) → B0, m_4, w12, n_4, w14
  26. Polygon(W3, W13, W1, W15) → B1, w3, w13, p_4, w15
  27. Polygon(W4, W16, W5, W17) → B2, w4, w16, w5, w17
  28. Polygon(W7, W19, W6, W18) → B3, w7, w19, w6, w18
  29. Polygon(W8, W21, W11, W22) → B4, w8, w21, w11, w22
  30. Polygon(W9, W20, W10, W23) → B5, w9, w20, w10, w23
  31. Polygon(W0, W8, W14) → B6, q_4, r_4, s_4
  32. Polygon(W1, W9, W15) → B7, t_4, a_4, b_4
  33. Polygon(W2, W10, W12) → B8, c_4, d_4, e_4
  34. Polygon(W3, W11, W13) → B9, f_5, g_5, h_5
  35. Polygon(W4, W0, W16) → B10, i_5, j_5, k_5
  36. Polygon(W5, W1, W17) → B11, l_5, m_5, n_5
  37. Polygon(W6, W2, W18) → B12, p_5, q_5, r_5
  38. Polygon(W7, W3, W19) → B13, s_5, t_5, a_5
  39. Polygon(W8, W4, W21) → B14, b_5, c_5, d_5
  40. Polygon(W9, W5, W20) → B15, e_5, f_6, g_6
  41. Polygon(W10, W6, W23) → B16, h_6, i_6, j_6
  42. Polygon(W11, W7, W22) → B17, k_6, l_6, m_6
  43. Polygon(W13, W17, W1) → B19, r_6, s_6, t_6
  44. Polygon(W14, W18, W2) → B20, a_6, b_6, c_6
  45. Polygon(W15, W19, W3) → B21, d_6, e_6, f_7
  46. Polygon(W16, W20, W5) → B22, g_7, h_7, i_7
  47. Polygon(W17, W21, W4) → B23, j_7, k_7, l_7
  48. Polygon(W18, W22, W7) → B24, m_7, n_7, p_7
  49. Polygon(W19, W23, W6) → B25, q_7, r_7, s_7
  50. Polygon(W20, W12, W10) → B26, t_7, a_7, b_7
  51. Polygon(W22, W14, W8) → B28, c_7, d_7, e_7
  52. Polygon(W23, W15, W9) → B29, f_8, g_8, h_8
  53. Polygon(W8, W0, W4) → B30, i_8, j_8, k_8
  54. Polygon(W9, W1, W5) → B31, l_8, m_8, n_8
  55. Polygon(W10, W2, W6) → B32, p_8, q_8, r_8
  56. Polygon(W11, W3, W7) → B33, s_8, t_8, a_8
  57. Polygon(W12, W20, W16) → B34, b_8, c_8, d_8
  58. Polygon(W13, W21, W17) → B35, e_8, f_9, g_9
  59. Polygon(W14, W22, W18) → B36, h_9, i_9, j_9
  60. Polygon(W15, W23, W19) → B37, k_9, l_9, m_9
  61. Polygon(W12, W16, W0) → B18, n_6, p_6, q_6
  62. Sphere(O, r1e) → Kg1e
  63. Sphere(O, r1i) → Kg1i
  64. Sphere(O, r2c) → Kg2c
  65. Sphere(O, r2m) → Kg2m
  66. Polygon(W21, W13, W11) → B27, n_9, p_9, q_9
  67. Intersect(f, s_4) → S001
  68. Intersect(d_7, d_2) → S002
  69. Intersect(i_8, e_2) → S003
  70. Distance(V0, O) → r1c
  71. Sphere(O, r2sq) → Kg2sq
  72. Sphere(O, r2t) → Kg2t
  73. Intersect(h_9, a_2) → S004
  74. Intersect(j_9, j_2) → S005
  75. Intersect(h, c_6) → S006