积极 AI Logo 积极 AI

球体交集

球体交集
几何画板及绘图内容加载中，请稍等……
2015-04-15 20:32
解析几何立体几何几何作图
该范例演示了球体的交集或球面部分的并集。涉及的核心数学概念包括立体几何中的球体和球面。通过使用Circle, Intersect, Sphere, IntersectConic, If, Surface等命令，可以构造出球体的交集或球面部分的并集。适合高中或大学的立体几何学习。

GeoGebra 命令及参数

  1. Circle((0, 0), rb) → cb
  2. Circle((0, h), ra) → ca
  3. Intersect(ca, cb) → I_1, I_2, ,
  4. Sphere((0, 0, (-y(I_1))), rb) → sb
  5. Sphere((0, 0, h - y(I_1)), ra) → sa
  6. IntersectConic(sa, sb) → e
  7. If(Defined[e], Angle[(0, 0, -10), (0, 0, (-y(I_1))), Point[e, 0]], 1.5708) → β
  8. If(Defined[e], Angle[(0, 0, -20), (0, 0, h - y(I_1)), Point[e, 0]], 0) → α
  9. Surface(((ra * cos(u)) * cos(v)), ((ra * sin(u)) * cos(v)), h - y(I_1) + (ra * sin(v)), u, 0, 6.28319, v, -1.5708, ((-π)) / 2 + α) → a
  10. Surface(((rb * cos(u)) * cos(v)), ((rb * sin(u)) * cos(v)), (-y(I_1)) + (rb * sin(v)), u, 0, 6.28319, v, ((-π)) / 2 + β, 1.5708) → b
  11. Surface(((rb * cos(u)) * cos(v)), ((rb * sin(u)) * cos(v)), (-y(I_1)) + (rb * sin(v)), u, 0, 6.28319, v, ((-π)) / 2 + β, 1.5208) → bbb
  12. Surface(((rb * cos(u)) * cos(v)), ((rb * sin(u)) * cos(v)), (-y(I_1)) + (rb * sin(v)), u, 0, 6.29, v, ((-π)) / 2 + β, 1.5208) → bb
  13. Surface(((ra * cos(u)) * cos(v)), ((ra * sin(u)) * cos(v)), h - y(I_1) + (ra * sin(v)), u, 0, 6.28319, v, -1.58, ((-π)) / 2 + α) → aa
  14. Surface(((ra * cos(u)) * cos(v)), ((ra * sin(u)) * cos(v)), h - y(I_1) + (ra * sin(v)), u, 0, 6.28, v, -1.5708, ((-π)) / 2 + α) → aaa