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Sphere Cross Section Investigation

Sphere Cross Section Investigation
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2016-01-12 21:13
CircleCoordinate GeometrySolid GeometryGeometric Construction
In collections Cross Sections
This example demonstrates the investigation of cross sections created by intersecting a sphere with a plane. It involves core mathematical concepts such as sphere, plane, cross section, circle, and coordinate geometry. The construction utilizes GeoGebra commands like Intersect, Sphere, Circle, Segment, PointIn, Plane, and IntersectPath. It is suitable for high school students studying solid geometry and analytical geometry, providing a visual understanding of the geometric relationships between spheres and planes.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → C_1
  2. Sphere(C_1, 2) → a
  3. Circle(C_1, 2, zAxis) → d
  4. Circle(C_1, 2, xAxis) → e
  5. Intersect(zAxis, e) → A_1, B_1
  6. Intersect(yAxis, d) → C_2, D
  7. Segment(C_1, D) → f
  8. Segment(C_1, A_1) → g
  9. PointIn(a) → A
  10. PointIn(a) → B
  11. PointIn(a) → C
  12. Plane(A, B, C) → h
  13. IntersectPath(h, a) → k
  14. IntersectPath(h, a) → p