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Dini's Surface by Roman Chijner

Dini's Surface by Roman Chijner
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2014-12-30 20:11
Solid GeometryTransformationParametric Equation
This example demonstrates the construction of Dini's surface, a doubly ruled surface with a spiral twist. It involves key mathematical concepts such as parametric equations and solid geometry. Using GeoGebra commands like Sequence, Join, RemoveUndefined, and Surface, the parameters of the surface can be dynamically adjusted to observe changes. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[(u_{min} + (i * dx), v_{min} + (j * dy)), i, 0, Na], j, 0, Na) → l1a
  2. Join(l1a) → uv
  3. RemoveUndefined(X1) → X1E
  4. RemoveUndefined(Y1) → Y1E
  5. RemoveUndefined(Z1) → Z1E
  6. Textfield(X1) → inputBox1
  7. Textfield(Y1) → inputBox2
  8. Textfield(Z1) → inputBox3
  9. Max(X1E) → x1maxa
  10. Min(X1E) → x1mina
  11. Max(Y1E) → x2maxa
  12. Min(Y1E) → x2mina
  13. Max(Z1E) → x3maxa
  14. Min(Z1E) → x3mina
  15. Textfield(N) → inputBox6
  16. Surface(((r_X * cos(v)) * cos(u)), (((r_Y * 5) * sin(u)) * sin(v)), ((r_Z * 5) * (cos(v) + log(tan(v / 2)))) + (1.3 * u), u, u_{min}, u_{max}, v, v_{min}, v_{max}) → h