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Intersection of a Cylinder and a Sphere

Intersection of a Cylinder and a Sphere
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2016-09-08 13:25
Solid GeometryGeometric ConstructionGraphing
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the intersection of a cylinder and a sphere using dynamic geometry. It illustrates the shape of the intersection curve. Key math concepts include solid geometry, spatial geometric relationships, and intersection calculations. The construction utilizes GeoGebra commands/objects such as Circle, Surface, Point, OrthogonalLine, Intersect, Segment, Sphere, and Locus. Suitable for high school students and math enthusiasts to understand the properties and transformations of intersecting spatial geometric bodies.

GeoGebra Commands & Parameters

  1. Circle((0, 0, (-h)), R', xOyPlane) → p
  2. Circle((0, 0, h), R', xOyPlane) → k
  3. Surface((R' * cos(u)), (R' * sin(u)), t, u, 0, (2 * π), t, (-h), h) → b
  4. Circle((0, 0), R') → c
  5. Point(c) → B
  6. OrthogonalLine(B, xOyPlane) → i
  7. Intersect(i, p) → F,
  8. Intersect(i, k) → G,
  9. Segment(F, G) → l
  10. Sphere(A, R) → d
  11. Intersect(l, d) → D, C
  12. Locus(D, B) → LG2
  13. Locus(C, B) → LG1