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旋转体与体积可视化

旋转体与体积可视化
几何画板及绘图内容加载中，请稍等……
2016-01-03 08:43
函数立体几何微积分
这个GeoGebra范例演示了由曲线y=x^2、x轴和y轴围成的区域绕x轴旋转生成的旋转体。涉及的核心数学概念包括函数、立体几何和微积分。通过使用CurveCartesian、Surface、Polygon等命令，可以构造旋转体的图像。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. CurveCartesian(t, 0, t^(2), t, 0, 2) → a
  2. CurveCartesian(t, 0, 4, t, 0, 2) → b
  3. Surface((t * cos(s)), (t * sin(s)), t^(2), t, 0, 2, s, 0, theta) → e
  4. CurveCartesian((t * cos(theta)), (t * sin(theta)), 4, t, 0, 2) → d
  5. Surface((t * cos(s)), (t * sin(s)), 4, t, 0, 2, s, 0, theta) → c
  6. Polygon((0.5, 0, 0.5^(2)), (0.7, 0, 0.5^(2)), (0.7, 0, 4), (0.5, 0, 4)) → poly1, h, i, j, k
  7. Surface((0.5 * cos(s)), (0.5 * sin(s)), t^(2), t, 0.5, 2, s, 0, theta) → f
  8. Surface((0.7 * cos(s)), (0.7 * sin(s)), t^(2), t, 0.5, 2, s, 0, theta) → g
  9. Polygon(((0.5 * cos(theta)), (0.5 * sin(theta)), 0.5^(2)), ((0.7 * cos(theta)), (0.7 * sin(theta)), 0.5^(2)), ((0.7 * cos(theta)), (0.7 * sin(theta)), 4), ((0.5 * cos(theta)), (0.5 * sin(theta)), 4)) → poly2, l, m, n, p
  10. Surface((r * cos(s)), (r * sin(s)), 4, r, 0.5, 0.7, s, 0, theta) → o
  11. Surface((r * cos(s)), (r * sin(s)), 0.5^(2), r, 0.5, 0.7, s, 0, theta) → q
  12. Polygon((0, 0, 2), (sqrt(2), 0, 2), (sqrt(2), 0, 2.2), (0, 0, 2.2)) → poly3, r, s, t, a_1
  13. Polygon((0, 0, 2), ((sqrt(2) * cos(theta)), sin(theta), 2), ((sqrt(2) * cos(theta)), sin(theta), 2.2), (0, 0, 2.2)) → poly4, b_1, c_1, d_1, e_1
  14. Surface((t * cos(s)), (t * sin(s)), 2, t, 0, sqrt(2), s, 0, theta) → u
  15. Surface((t * cos(s)), (t * sin(s)), 2.2, t, 0, sqrt(2), s, 0, theta) → v
  16. Surface((sqrt(2) * cos(s)), (sqrt(2) * sin(s)), t, t, 2, 2.2, s, 0, theta) → w
  17. CurveCartesian((t * cos(theta)), (t * sin(theta)), t^(2), t, 0, 2) → g_1