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圆柱的展开图 by Michael Bailey

圆柱的展开图 by Michael Bailey
几何画板及绘图内容加载中，请稍等……
2015-04-07 09:47
圆立体几何几何作图
所属专题 Chapter 11: Surface Area and Volume
这个范例演示了圆柱的展开图。涉及的核心数学概念包括立体几何和几何作图。通过使用GeoGebra命令如Circle, Line, Rotate等，可以动态展示圆柱侧面展开的过程。适合初中及以上学生学习立体几何。

GeoGebra 命令及参数

  1. Circle((0, 0, 3), (1, -1, 3), (0, -2, 3)) → c
  2. If(t < 1, Surface[(r * sin((t * θ))), ((-r) * (1 - cos((t * θ)))), u, t, -3.14159, 3.141592653589793, u, 0, 3], Surface[t, 0, u, t, -3.14159, 3.141592653589793, u, 0, 3]) → a
  3. Line(A, B) → b
  4. Rotate(c, (-α), b) → c'
  5. Circle((0, 0, 0), (1, -1, 0), (0, -2, 0)) → d
  6. Rotate(d, (-α), y = 0) → d'
  7. If(t < 1, ((r * sin((π * θ))), ((-r) * (1 - cos((π * θ)))), 3), (3.141592653589793, 0, 3)) → C
  8. If(t < 1, ((r * sin((π * θ))), ((-r) * (1 - cos((π * θ)))), 0), (3.141592653589793, 0, 0)) → D
  9. Midpoint(C, D) → E
  10. Segment(C, D) → e
  11. Rotate(F, (-α), b) → F'
  12. Midpoint(G, F') → H
  13. Rotate(c, (-α), b) → c'_1
  14. Rotate(d, (-α), y = 0) → d'_1
  15. If(t < 1, CurveCartesian[(r * sin((t * θ))), ((-r) * (1 - cos((t * θ)))), 0, t, -3.14159, 3.141592653589793], CurveCartesian[t, 0, 0, t, -3.14159, 3.141592653589793]) → f
  16. If(t < 1, CurveCartesian[(r * sin((t * θ))), ((-r) * (1 - cos((t * θ)))), 3, t, -3.14159, 3.141592653589793], CurveCartesian[t, 0, 3, t, -3.14159, 3.141592653589793]) → g
  17. Segment((0, -2, 0), (0, -2, 3)) → h
  18. If(t < 1, ((r * sin(((-π) * θ))), ((-r) * (1 - cos(((-π) * θ)))), 3), (-3.141592653589793, 0, 3)) → I
  19. If(t < 1, ((r * sin(((-π) * θ))), ((-r) * (1 - cos(((-π) * θ)))), 0), (-3.141592653589793, 0, 0)) → J
  20. Segment(I, J) → j

AI 绘图提示语参考

绘制一个圆柱体的展开图，首先画一个底面圆，然后围绕圆心旋转生成侧面，接着画另一个底面圆并旋转生成侧面，最后连接两个侧面的圆周，形成展开图。
以上提示语为根据原始绘图命令整理而来，仅供参考。