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Sphere-Cylinder Intersection

Sphere-Cylinder Intersection
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2018-04-04 07:02
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the intersection of a sphere and a cylinder, showcasing their spatial relationship. Key mathematical concepts include solid geometry, intersection, rotational bodies, and analytical geometry. GeoGebra commands used in construction are Sphere, Circle, CurveCartesian, and Surface. Suitable for high school students and math enthusiasts to understand the properties of intersection points and shapes of spatial geometric bodies.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), r) → e
  2. Circle((r, 0, (-2 * r)), r, zAxis) → f
  3. CurveCartesian(a + ((r - a) * cos(t)), ((r - a) * sin(t)), ((-2 * sqrt((a * (r - a)))) * sin(t / 2)), t, 0, (4 * π)) → int
  4. Surface(a + ((r - a) * cos(u)), ((r - a) * sin(u)), v, u, 0, (2 * π), v, (-r), r) → i