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圆柱的分割

圆柱的分割
几何画板及绘图内容加载中，请稍等……
2016-02-28 21:41
函数立体几何几何作图
这个范例演示了如何通过调整圆柱的高度和半径来分割圆柱。核心数学概念包括几何构造、立体几何和函数。使用了If, Cylinder, Surface等GeoGebra命令。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. If(a < 1, a / sin(π / n), If[a ≥ 4, (5 - a) / sin(π / n), 1 / sin(π / n)]) → b
  2. If(a < 1, 0, If[a < 2, a - 1, 1]) → c
  3. If(a < 2, 0, If[a < 3, a - 2, 1]) → d
  4. If(a < 3, 0, If[a < 4, a - 3, 1]) → e
  5. Cylinder((0, 0, ((-h)) / 2), (0, 0, h / 2), r) → g, k, p, i
  6. Surface((r * cos(u + (((c * 2) * π / n) * 0))) + ((b * r) * cos(π / n)), (r * sin(u + (((c * 2) * π / n) * 0))) + ((b * r) * sin(π / n)), v - ((0 * d) * h / n) + ((0 * e) * h / n), u, (0 * π / n), (2 * π / n), v, ((-h)) / 2 + (0 * h / n), ((-h)) / 2 + h / n) → s_{0}
  7. Surface((r * cos(u + ((c * 2) * π / n))) + ((b * r) * cos(π / n)), (r * sin(u + ((c * 2) * π / n))) + ((b * r) * sin(π / n)), v - (d * h / n) + ((0 * e) * h / n), u, (0 * π / n), (2 * π / n), v, ((-h)) / 2 + h / n, ((-h)) / 2 + (2 * h / n)) → s_{1}
  8. Surface((r * cos(u + (((c * 2) * π / n) * 2))) + ((b * r) * cos(π / n)), (r * sin(u + (((c * 2) * π / n) * 2))) + ((b * r) * sin(π / n)), v - ((2 * d) * h / n) + ((0 * e) * h / n), u, (0 * π / n), (2 * π / n), v, ((-h)) / 2 + (2 * h / n), ((-h)) / 2 + (3 * h / n)) → s_{2}
  9. Surface((r * cos(u + (((c * 2) * π / n) * 0))) + ((b * r) * cos((3 * π / n))), (r * sin(u + (((c * 2) * π / n) * 0))) + ((b * r) * sin((3 * π / n))), v - ((0 * d) * h / n) + (e * h / n), u, (2 * π / n), (4 * π / n), v, ((-h)) / 2 + (0 * h / n), ((-h)) / 2 + h / n) → s_{10}
  10. Surface((r * cos(u + ((c * 2) * π / n))) + ((b * r) * cos((3 * π / n))), (r * sin(u + ((c * 2) * π / n))) + ((b * r) * sin((3 * π / n))), v - (d * h / n) + (e * h / n), u, (2 * π / n), (4 * π / n), v, ((-h)) / 2 + h / n, ((-h)) / 2 + (2 * h / n)) → s_{11}
  11. Surface((r * cos(u + (((c * 2) * π / n) * 2))) + ((b * r) * cos((3 * π / n))), (r * sin(u + (((c * 2) * π / n) * 2))) + ((b * r) * sin((3 * π / n))), v - ((2 * d) * h / n) + (e * h / n), u, (2 * π / n), (4 * π / n), v, ((-h)) / 2 + (2 * h / n), ((-h)) / 2 + (3 * h / n)) → s_{12}
  12. Surface((r * cos(u + (((c * 2) * π / n) * 0))) + ((b * r) * cos((5 * π / n))), (r * sin(u + (((c * 2) * π / n) * 0))) + ((b * r) * sin((5 * π / n))), v - ((0 * d) * h / n) + ((2 * e) * h / n), u, (4 * π / n), (6 * π / n), v, ((-h)) / 2 + (0 * h / n), ((-h)) / 2 + h / n) → s_{20}
  13. Surface((r * cos(u + ((c * 2) * π / n))) + ((b * r) * cos((5 * π / n))), (r * sin(u + ((c * 2) * π / n))) + ((b * r) * sin((5 * π / n))), v - (d * h / n) + ((2 * e) * h / n), u, (4 * π / n), (6 * π / n), v, ((-h)) / 2 + h / n, ((-h)) / 2 + (2 * h / n)) → s_{21}
  14. Surface((r * cos(u + (((c * 2) * π / n) * 2))) + ((b * r) * cos((5 * π / n))), (r * sin(u + (((c * 2) * π / n) * 2))) + ((b * r) * sin((5 * π / n))), v - ((2 * d) * h / n) + ((2 * e) * h / n), u, (4 * π / n), (6 * π / n), v, ((-h)) / 2 + (2 * h / n), ((-h)) / 2 + (3 * h / n)) → s_{22}
  15. Surface(((v * r) * cos(u + (((c * 2) * π / n) * 0))) + ((b * r) * cos(π / n)), ((v * r) * sin(u + (((c * 2) * π / n) * 0))) + ((b * r) * sin(π / n)), ((-h)) / 2 + h / n - ((0 * d) * h / n) + ((0 * e) * h / n), u, (0 * π / n), (2 * π / n), v, 0, 1) → sh_{0}
  16. Surface(((v * r) * cos(u + ((c * 2) * π / n))) + ((b * r) * cos(π / n)), ((v * r) * sin(u + ((c * 2) * π / n))) + ((b * r) * sin(π / n)), ((-h)) / 2 + (2 * h / n) - (d * h / n) + ((0 * e) * h / n), u, (0 * π / n), (2 * π / n), v, 0, 1) → sh_{1}
  17. Surface(((v * r) * cos(u + (((c * 2) * π / n) * 2))) + ((b * r) * cos(π / n)), ((v * r) * sin(u + (((c * 2) * π / n) * 2))) + ((b * r) * sin(π / n)), ((-h)) / 2 + (3 * h / n) - ((2 * d) * h / n) + ((0 * e) * h / n), u, (0 * π / n), (2 * π / n), v, 0, 1) → sh_{2}
  18. Surface(((v * r) * cos(u + (((c * 2) * π / n) * 0))) + ((b * r) * cos((3 * π / n))), ((v * r) * sin(u + (((c * 2) * π / n) * 0))) + ((b * r) * sin((3 * π / n))), ((-h)) / 2 + h / n - ((0 * d) * h / n) + (e * h / n), u, (2 * π / n), (4 * π / n), v, 0, 1) → sh_{10}
  19. Surface(((v * r) * cos(u + ((c * 2) * π / n))) + ((b * r) * cos((3 * π / n))), ((v * r) * sin(u + ((c * 2) * π / n))) + ((b * r) * sin((3 * π / n))), ((-h)) / 2 + (2 * h / n) - (d * h / n) + (e * h / n), u, (2 * π / n), (4 * π / n), v, 0, 1) → sh_{11}
  20. Surface(((v * r) * cos(u + (((c * 2) * π / n) * 2))) + ((b * r) * cos((3 * π / n))), ((v * r) * sin(u + (((c * 2) * π / n) * 2))) + ((b * r) * sin((3 * π / n))), ((-h)) / 2 + (3 * h / n) - ((2 * d) * h / n) + (e * h / n), u, (2 * π / n), (4 * π / n), v, 0, 1) → sh_{12}
  21. Surface(((v * r) * cos(u + (((c * 2) * π / n) * 0))) + ((b * r) * cos((5 * π / n))), ((v * r) * sin(u + (((c * 2) * π / n) * 0))) + ((b * r) * sin((5 * π / n))), ((-h)) / 2 + h / n - ((0 * d) * h / n) + ((2 * e) * h / n), u, (4 * π / n), (6 * π / n), v, 0, 1) → sh_{20}
  22. Surface(((v * r) * cos(u + ((c * 2) * π / n))) + ((b * r) * cos((5 * π / n))), ((v * r) * sin(u + ((c * 2) * π / n))) + ((b * r) * sin((5 * π / n))), ((-h)) / 2 + (2 * h / n) - (d * h / n) + ((2 * e) * h / n), u, (4 * π / n), (6 * π / n), v, 0, 1) → sh_{21}
  23. Surface(((v * r) * cos(u + (((c * 2) * π / n) * 2))) + ((b * r) * cos((5 * π / n))), ((v * r) * sin(u + (((c * 2) * π / n) * 2))) + ((b * r) * sin((5 * π / n))), ((-h)) / 2 + (3 * h / n) - ((2 * d) * h / n) + ((2 * e) * h / n), u, (4 * π / n), (6 * π / n), v, 0, 1) → sh_{22}