动态可调的开口长方体打包项目

动态可调的开口长方体打包项目
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2020-03-24 19:48
①本范例演示了如何动态构建和修改开口长方体的形状与体积;②涉及的核心数学概念包括优化问题、体积计算、单位圆、函数图像、几何变换、阶跃函数和相关性;③作图要点:利用了Intersect(相交)、Segment(线段)、Point(点)、Mirror(镜像)、Circle(圆)、Polygon(多边形)、Rotate(旋转)等GeoGebra命令;④适合高中及以上学生学习和理解立体几何、优化问题及动态几何变换。

GeoGebra 命令及参数

  1. Intersect(l, xAxis) → E
  2. Intersect(j, l) → F
  3. Segment(A, F) → m
  4. Point(m) → G
  5. Mirror(G, j) → G'
  6. Mirror(G, k) → G'_1
  7. Mirror(G', k) → G''
  8. Segment(A, G) → n
  9. Circle(A, G) → c
  10. Intersect(c, r, 1) → H
  11. Intersect(p, s) → I
  12. Mirror(H, k) → H'
  13. Mirror(I, k) → I'
  14. Mirror(I, j) → I'_1
  15. Mirror(H, j) → H'_1
  16. Mirror(I'_1, k) → J
  17. Mirror(H'_1, k) → K
  18. Segment(I', J) → t
  19. Segment(J, I'_1) → a
  20. Segment(I'_1, I) → b
  21. Segment(I, I') → d
  22. Segment(A, B) → e
  23. Segment(A, H) → n_1
  24. Polygon(G, G', I'_1, I) → poly2, g_1, g', i'_1, i_1
  25. Polygon(I, H, H', I') → poly3, i_2, h_1, h', i'
  26. Polygon(I', G'_1, G'', J) → poly4, i'_2, g'_1, g'', j_1
  27. Polygon(J, K, H'_1, I'_1) → poly5, j_2, k_1, h'_1, i'_3
  28. Polygon(I, I'_1, J, I') → poly6, i_3, i'_4, j_3, i'_5
  29. Segment(I, I'_1) → p_1
  30. Segment(I'_1, J) → q_1
  31. Segment(J, I') → r_1
  32. Segment(I', I) → s_1
  33. Rotate(G, α, b) → G'_2
  34. Rotate(G', α, b) → G''_1
  35. Rotate(I'_1, α, b) → L
  36. Rotate(I, α, b) → I'_2
  37. Polygon(G'_2, G''_1, L, I'_2) → poly2', g'_2, g''_1, l_2, i'_6
  38. Rotate(J, α, x = x(J)) → J'
  39. Rotate(K, α, x = x(J)) → K'
  40. Rotate(I'_1, α, x = x(J)) → N
  41. Rotate(J, (-α), x = x(J)) → J'_1
  42. Rotate(K, (-α), x = x(J)) → K'_1
  43. Rotate(H'_1, (-α), x = x(J)) → O
  44. Rotate(I'_1, (-α), x = x(J)) → P
  45. Polygon(J'_1, K'_1, O, P) → poly5'_1, j'_1, k'_1, o, p_2
  46. Rotate(I', (-α), y = y(H')) → I''_1
  47. Rotate(G'_1, (-α), y = y(H')) → Q
  48. Rotate(G'', (-α), y = y(H')) → G'''_1
  49. Rotate(J, (-α), y = y(H')) → J'_3
  50. Polygon(I''_1, Q, G'''_1, J'_3) → poly4'_1, i''_1, q_2, g'''_1, j'_3
  51. Rotate(I, α, x = x(G)) → I'_3
  52. Rotate(H, α, x = x(G)) → H'_2
  53. Rotate(H', α, x = x(G)) → H''
  54. Rotate(I', α, x = x(G)) → I''
  55. Polygon(I'_3, H'_2, H'', I'') → poly3', i'_7, h'_2, h'', i''
  56. Rotate(A, ((-π)) / 2, B) → A'
  57. Rotate(B, ((-π)) / 2, B) → B'
  58. Segment(A', B') → e'
  59. Rotate(A', ((-π)) / 2, A') → A''
  60. Rotate(B', ((-π)) / 2, A') → B''
  61. Segment(A'', B'') → e''
  62. Rotate(A'', ((-π)) / 2, B'') → A'''
  63. Rotate(B'', ((-π)) / 2, B'') → B'''
  64. Segment(A''', B''') → e'''

AI 绘图提示语参考

画一个开口向上的长方体,动态展示其体积优化和几何变换。首先绘制长方体的底面和侧面,然后通过镜像和旋转操作创建顶部的几何形状,最后将所有部分组合成一个完整的开口长方体。展示过程中注意几何变换和体积变化的关系,以及如何通过函数图和单位圆来辅助理解和优化。
以上提示语为根据原始绘图命令整理而来,仅供参考。