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自定义长方体：体积/表面积的可变长度

自定义长方体：体积/表面积的可变长度
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2016-03-21 23:45
立体几何几何作图
①本范例演示可自定义尺寸的长方体，用于教学体积与表面积计算；②涉及核心数学概念：立体几何、体积公式、表面积公式；③作图要点：使用Segment、OrthogonalLine、Intersect、Ray、Circle、Line、Vector、Polygon、Sequence等GeoGebra命令构建几何体及动态元素；④适合初中及以上数学教学或几何学习，支持滑块调节尺寸、网格显示、实体/透明切换及对应对称面着色。

GeoGebra 命令及参数

  1. Segment(A, C) → i
  2. Segment(A, B) → d
  3. OrthogonalLine(B, d) → e
  4. OrthogonalLine(C, i) → f
  5. Intersect(e, f) → D
  6. Segment(D, C) → g
  7. Segment(D, B) → h
  8. Ray(C, E) → p
  9. Ray(D, E) → q
  10. Ray(B, E) → r
  11. Circle(D, (0.6 * c)) → s
  12. Intersect(s, q) → I,
  13. Line(I, h) → j
  14. Line(I, g) → k
  15. Intersect(j, r) → F
  16. Intersect(k, p) → G
  17. Segment(F, I) → l
  18. Segment(I, G) → m
  19. Segment(F, B) → n
  20. Segment(I, D) → t
  21. Segment(G, C) → a_1
  22. Line(G, l) → b_1
  23. Line(F, m) → c_1
  24. Intersect(c_1, b_1) → H
  25. Segment(F, H) → d_1
  26. Segment(H, G) → e_1
  27. Segment(H, A) → f_1
  28. Vector(J, K) → u
  29. Polygon(F, I, G, H) → poly1, f_2, i_1, g_1, h_1
  30. Polygon(B, D, C, A) → poly2, b_2, d_2, c_2, a_2
  31. Polygon(F, B, A, H) → poly3, f_3, b_3, a_3, h_2
  32. Polygon(I, D, C, G) → poly4, i_2, d_3, c_3, g_2
  33. Polygon(F, I, D, B) → poly5, f_4, i_3, d_4, b_4
  34. Polygon(H, G, C, A) → poly6, h_3, g_3, c_4, a_4
  35. Sequence(Segment[(x(C) + (k / c * (x(G) - x(C))), y(C) + (k / c * (y(G) - y(C)))), (x(D) + (k / c * (x(I) - x(D))), y(D) + (k / c * (y(I) - y(D))))], k, 1, c - 1) → list2
  36. Sequence(Segment[(x(A) + (k / b * (x(C) - x(A))), y(A) + (k / b * (y(C) - y(A)))), (x(B) + (k / b * (x(D) - x(B))), y(B) + (k / b * (y(D) - y(B))))], k, 1, b - 1) → list3
  37. Sequence(Segment[(x(A) + (k / a * (x(B) - x(A))), y(A) + (k / a * (y(B) - y(A)))), (x(C) + (k / a * (x(D) - x(C))), y(C) + (k / a * (y(D) - y(C))))], k, 1, a - 1) → list4
  38. Sequence(Segment[(x(C) + (k / a * (x(D) - x(C))), y(C) + (k / a * (y(D) - y(C)))), (x(G) + (k / a * (x(I) - x(G))), y(G) + (k / a * (y(I) - y(G))))], k, 1, a - 1) → list5
  39. Sequence(Segment[(x(D) + (k / c * (x(I) - x(D))), y(D) + (k / c * (y(I) - y(D)))), (x(B) + (k / c * (x(F) - x(B))), y(B) + (k / c * (y(F) - y(B))))], k, 1, c - 1) → list6
  40. Sequence(Segment[(x(F) + (k / b * (x(I) - x(F))), y(F) + (k / b * (y(I) - y(F)))), (x(B) + (k / b * (x(D) - x(B))), y(B) + (k / b * (y(D) - y(B))))], k, 1, b - 1) → list1