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Concentric Spheres Cut by a Plane

Concentric Spheres Cut by a Plane
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2018-06-21 04:31
CircleSolid GeometryGeometric Construction
This example demonstrates the geometric phenomenon of concentric spheres being cut by a plane. Key mathematical concepts include spheres, plane geometry, and solid geometry. Using GeoGebra commands such as Intersect, Point, Sphere, etc., multiple concentric spheres are constructed and the intersection lines when cut by a plane are observed. Suitable for high school students and educators for teaching and learning solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(zAxis) → B
  3. Sphere(A, B) → a
  4. Point(zAxis) → C
  5. Sphere(A, C) → b
  6. Point(zAxis) → D
  7. OrthogonalPlane(D, zAxis) → c
  8. IntersectPath(c, a) → d
  9. IntersectPath(c, b) → e
  10. Area(e) → f
  11. PointIn(e) → Pointe
  12. Area(d) → g
  13. PointIn(d) → Pointd
  14. Point(e) → E
  15. Tangent(E, d) → i, j
  16. Intersect(i, e) → F, G
  17. Point(i) → H
  18. Segment(H, E) → k
  19. Segment(F, G) → l
  20. Segment(hide, show) → m
  21. Point(m) → R
  22. Distance(hide, R) → distancePR