MathPlotAI Logo MathPlotAI

Cross Sections of a Sphere

Cross Sections of a Sphere
Loading the math board and drawing, please wait…
2020-03-05 00:48
Coordinate GeometrySolid GeometryGeometric Construction
In collections Cross Sections
This example demonstrates the cross sections of a sphere. Key mathematical concepts include solid geometry and coordinate geometry. Using GeoGebra commands such as Intersect, Point, Cone, Plane, PointIn, Line, Circle, CircleArc, Segment, OrthogonalLine, Sphere, OrthogonalPlane, and IntersectPath, the construction of a sphere and its cross sections is achieved. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  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