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球体的截面 by Stephanie Bagley

球体的截面 by Stephanie Bagley
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2020-03-05 00:48
解析几何立体几何几何作图
所属专题 Cross Sections
这个范例演示了球体的截面。核心数学概念包括立体几何和解析几何。通过使用Intersect, Point, Cone, Plane, PointIn, Line, Circle, CircleArc, Segment, OrthogonalLine, Sphere, OrthogonalPlane, IntersectPath等GeoGebra命令，可以构造出球体及其截面。适合高中或大学的立体几何课程。

GeoGebra 命令及参数

  1. Intersect(yAxis, xAxis) → A
  2. Point(zAxis) → F
  3. Intersect(zAxis, xAxis) → E
  4. Cone(E, F, 1) → TheCone, r, i
  5. Point(xAxis) → I
  6. Point(xAxis) → K
  7. Point(zAxis) → O
  8. Plane(I, K, O) → p
  9. PointIn(p) → CenterOfNormalAngle
  10. Line(CenterOfNormalAngle, xAxis) → g
  11. Circle(CenterOfNormalAngle, 0.25, p) → c
  12. Intersect(g, c) → i_{2}, i_1
  13. CircleArc(CenterOfNormalAngle, i_{2}, i_1, p) → ArcForPlaneAngle
  14. Point(ArcForPlaneAngle) → NormalAngleHandle
  15. Segment(CenterOfNormalAngle, NormalAngleHandle) → NormalSeg
  16. Point(zAxis) → B
  17. Circle(CenterOfNormalAngle, 0.25, p) → d
  18. Point(yAxis) → J
  19. Plane(I, J, K) → q
  20. OrthogonalLine(CenterOfNormalAngle, g, p) → h
  21. Point(zAxis) → C
  22. Intersect(yAxis, zAxis) → D
  23. Sphere(C, 1) → TheSphere
  24. PointIn(TheSphere) → H
  25. OrthogonalPlane(H, NormalSeg) → PerPenPlane
  26. IntersectPath(PerPenPlane, TheSphere) → e