正方体在平面上的投影

正方体在平面上的投影
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2019-05-24 15:01
这个范例演示了正方体在平面上的投影。核心数学概念包括立体几何和投影变换。通过使用GeoGebra命令如Circle, Point, Angle, Segment等,可以构造出正方体及其投影。适合高中或大学的立体几何课程使用。

GeoGebra 命令及参数

  1. Circle(I_1, 0.6) → k_2
  2. Point(k_2) → K_1
  3. Point(k_2) → J_1
  4. Angle(J_1, I_1, K_1) → b_1
  5. Circle(I, 0.6) → k_1
  6. Point(k_1) → K
  7. Point(k_1) → J
  8. Angle(J, I, K) → a_1
  9. Segment(A', B') → i
  10. Segment(B', C') → j
  11. Segment(C', D') → k
  12. Segment(D', A') → l
  13. Segment(B', F') → m
  14. Segment(F', E') → n
  15. Segment(A', E') → p
  16. Segment(E', H') → r
  17. Segment(G', H') → s
  18. Segment(G', F') → t
  19. Segment(G', C') → i_1
  20. Segment(H', D') → j_1
  21. Ray(A', A) → l_1
  22. Ray(B', B) → m_1
  23. Ray(F', F) → n_1
  24. Ray(E', E) → p_1
  25. Ray(G', G) → q_1
  26. Ray(H', H) → r_1
  27. Ray(D', D) → s_1
  28. Ray(C', C) → t_1
  29. Ellipse(L, M, N) → p_2
  30. Segment(A, B) → c
  31. Segment(A, E) → d
  32. Segment(E, F) → e
  33. Segment(B, F) → f
  34. Segment(F, G) → g
  35. Segment(H, E) → h
  36. Segment(D, A) → c_1
  37. Segment(C, B) → d_1
  38. Segment(D, C) → e_1
  39. Segment(H, G) → f_1
  40. Segment(G, C) → g_1
  41. Segment(D, H) → h_1
  42. Polygon(A, B, C, D) → Vieleck1, a_2, b_2, c_2, d_2
  43. Polygon(A', B', C', D') → Vieleck2, a', b', c', d'
  44. Polygon(C, B, F, G) → Vieleck3, c_3, b_3, f_2, g_2
  45. Polygon(C', B', F', G') → Vieleck4, c'_1, b'_1, f', g'
  46. Polygon(C, D, H, G) → Vieleck5, c_4, d_3, h_2, g_3
  47. Polygon(C', G', H', D') → Vieleck6, c'_2, g'_1, h', d'_1
  48. Polygon(E, F, G, H) → Vieleck7, e_2, f_3, g_4, h_3
  49. Polygon(E', F', G', H') → Vieleck8, e', f'_1, g'_2, h'_1
  50. Polygon(A, B, F, E) → Vieleck9, a_3, b_4, f_4, e_3
  51. Polygon(A', B', F', E') → Vieleck10, a'_1, b'_2, f'_2, e'_1
  52. Polygon(A, D, H, E) → Vieleck11, a_4, d_4, h_4, e_4
  53. Polygon(A', D', H', E') → Vieleck12, a'_2, d'_2, h'_2, e'_2