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Intersection of Surface and Curve

Intersection of Surface and Curve
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2018-07-29 15:37
FunctionCoordinate GeometrySolid Geometry
This example demonstrates the intersection of a surface and a curve. Key mathematical concepts include coordinate geometry. Using GeoGebra commands such as Cylinder, CurveCartesian, and Surface, complex geometric shapes can be constructed. Suitable for high school mathematics education or research.

GeoGebra Commands & Parameters

  1. Cylinder((0, 0, -4), (0, 0, 4), 2) → e, f, g, h
  2. Cylinder((0, -4, 0), (0, 4, 0), 2) → a, a_2, a_3, a_4
  3. CurveCartesian((2 * cos(t)), (2 * sin(t)), (2 * sin(t)), t, 0, π) → b
  4. CurveCartesian((2 * cos(t)), (-2 * sin(t)), (2 * sin(t)), t, 0, π) → c
  5. CurveCartesian((2 * cos(t)), (-2 * sin(t)), (-2 * sin(t)), t, 0, π) → d
  6. CurveCartesian((2 * cos(t)), (2 * sin(t)), (-2 * sin(t)), t, 0, π) → i
  7. Surface((u * x(b(t))) + ((1 - u) * x(c(t))), (u * y(b(t))) + ((1 - u) * y(c(t))), (u * z(b(t))) + ((1 - u) * z(c(t))), t, 0, π, u, 0, 1) → j
  8. Surface((u * x(d(t))) + ((1 - u) * x(c(t))), (u * y(d(t))) + ((1 - u) * y(c(t))), (u * z(d(t))) + ((1 - u) * z(c(t))), t, 0, π, u, 0, 1) → k
  9. Surface((u * x(d(t))) + ((1 - u) * x(i(t))), (u * y(d(t))) + ((1 - u) * y(i(t))), (u * z(d(t))) + ((1 - u) * z(i(t))), t, 0, π, u, 0, 1) → l
  10. Surface((u * x(b(t))) + ((1 - u) * x(i(t))), (u * y(b(t))) + ((1 - u) * y(i(t))), (u * z(b(t))) + ((1 - u) * z(i(t))), t, 0, π, u, 0, 1) → m