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Intersection of Two Cylinders

Intersection of Two Cylinders
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2019-01-20 20:09
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the intersection of two cylinders. Key mathematical concepts include cylinders, quadratic equations, and solid geometry. Using GeoGebra commands such as Circle, Mirror, Surface, and CurveCartesian, the intersection of the cylinders can be constructed. Suitable for high school solid geometry courses.

GeoGebra Commands & Parameters

  1. Circle((((-h) * r), 0, c), r, xAxis) → e'
  2. Circle((0, ((-h) * r), (-c)), r, yAxis) → d
  3. Mirror(e', (0, 0, c)) → e
  4. Surface(v, (r * cos(u)), c + (r * sin(u)), u, 0, (2 * π), v, ((-h) * r), (h * r)) → cilx
  5. Mirror(d, (0, 0, (-c))) → d'
  6. Surface((r * cos(u)), v, (-c) + (r * sin(u)), u, 0, (2 * π), v, ((-h) * r), (h * r)) → cily
  7. CurveCartesian((r * cos(t)), sqrt(r^(2) - ((2 * c) + (r * sin(t)))^(2)), (-c) - (r * sin(t)), t, 0, (2 * π)) → a
  8. CurveCartesian((r * cos(t)), (-sqrt(r^(2) - ((2 * c) + (r * sin(t)))^(2))), (-c) - (r * sin(t)), t, 0, (2 * π)) → b