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圆柱坐标系体积元素

圆柱坐标系体积元素
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2019-09-01 10:52
三角函数解析几何立体几何微积分
①本范例演示了圆柱坐标系下体积元素的可视化；②涉及核心数学概念包括圆柱坐标系、体积微元、积分计算；③作图要点：使用Line、Point、Intersect、Circle、Segment、CircleArc、Cylinder等GeoGebra命令构建几何模型；④适合大学数学、物理专业学生学习多重积分和立体几何。

GeoGebra 命令及参数

  1. Line((0.8, 0.6, 1), B) → c
  2. Point(c) → C
  3. Line(E, C) → h
  4. Intersect(h, eq2) → J, K
  5. Line(D, A) → g
  6. Intersect(g, eq2) → N, O
  7. Line((1, 0, 1), A) → d
  8. Circle(zAxis, C) → e
  9. Intersect(d, e) → F,
  10. Line(D, B) → f
  11. Line(D, G) → i
  12. Intersect(f, eq2) → L, M
  13. Segment(D, B) → k
  14. Segment(D, A) → j
  15. Segment(A, O) → n
  16. Segment(B, M) → p
  17. CircleArc(D, A, B) → s
  18. CircleArc(D, O, M) → t
  19. CircleArc(D, I, K) → d_1
  20. Segment(C, K) → q
  21. Segment(O, I) → f_1
  22. Segment(M, K) → h_1
  23. Segment(B, C) → g_1
  24. Segment(E, C) → m
  25. Segment(E, F) → l
  26. Segment(F, I) → r
  27. CircleArc(D, F, C) → c_1
  28. Segment(A, F) → e_1
  29. Circle(zAxis, (sqrt(2), 0, -1)) → k_1
  30. Cylinder(k_1, o) → u, r_1, v
  31. Circle(zAxis, (1, 0, -1)) → q_1
  32. Cylinder(q_1, w) → a_1, t_1, b_1