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Function Revolution

Function Revolution
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2015-02-28 18:10
FunctionCoordinate GeometryCalculusIntegral
This example demonstrates the rotation of functions around the X-axis or Y-axis to generate solids of revolution. It involves core mathematical concepts such as functions, rotation, integral calculus, coordinate geometry, and calculus. The construction uses commands like CurveCartesian, Rotate, Textfield, and Surface. It is suitable for high school students and math enthusiasts learning about function rotation and integral geometry.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, f(t), 0, t, 0, max) → a
  2. Rotate(a, α, xAxis) → ax'
  3. CurveCartesian(t, g(t), 0, t, 0, max) → b
  4. Rotate(b, α, xAxis) → bx'
  5. Textfield(f) → ChampTexte1
  6. Textfield(g) → ChampTexte2
  7. Surface(u, (f(u) * cos(v)), (f(u) * sin(v)), u, 0, max, v, 0, 6.28319) → sax
  8. Surface(u, (g(u) * cos(v)), (g(u) * sin(v)), u, 0, max, v, 0, 6.28319) → sbx
  9. Rotate(a, α, yAxis) → ay'
  10. Surface((u * cos(v)), f(u), (u * sin(v)), u, 0, max, v, 0, 6.28319) → say
  11. Rotate(b, α, yAxis) → by'
  12. Surface((u * cos(v)), g(u), (u * sin(v)), u, 0, max, v, 0, 6.28319) → sby