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Rotating Surface

Rotating Surface
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2018-05-30 12:22
FunctionSolid GeometryParametric Equation
In collections surface 3D /3D-Oberflächen 1
This example demonstrates how to draw a rotating surface in GeoGebra. It involves the principles of generating a rotating surface and how to construct such a solid geometry figure using functions and parametric equations. By adjusting parameters, different shapes of rotating surfaces can be observed. Suitable for high school mathematics education and students learning solid geometry.

GeoGebra Commands & Parameters

  1. CurveCartesian((r / n * ((n * cos(t)) + cos((n * t)))), (r / n * ((n * sin(t)) + sin((n * t)))), t, 0, (2 * π)) → a
  2. Surface(((r / n * ((n * cos(u)) + cos((n * u)))) * sin(v)), ((r / n * ((n * sin(u)) + sin((n * u)))) * sin(v)), (r * cos(v)), u, 0, (2 * π), v, 0, π) → b
  3. CurveCartesian(b(t, p_m), t, p_m, p_p) → c
  4. Surface(b(t, s), t, p_m, p_p, s, 0, p_m) → f
  5. CurveCartesian(b(t, π / 3), t, π / 3, p_p) → g
  6. Sequence(CurveCartesian[b(t, k), t, k, p_p], k, 0, p_m, 0.05) → lli_1
  7. Length(lli_1) → h
  8. CurveCartesian(b(t, p_m), t, p_p, p_m) → k
  9. Surface(b((k * t) + ((1 - k) * p_p), t), k, 0, 1, t, p_m', p_m) → j
  10. CurveCartesian(b(t, p_m'), t, p_p, p_m') → l
  11. CurveCartesian(b(p_p, t), t, p_m', p_m) → e
  12. CurveCartesian(b(t, t), t, p_m', p_m) → d
  13. CurveCartesian(b(t, p_m'), t, p_m', p_p) → m