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Dini's Surface (composed of points 51*51)

Dini's Surface (composed of points 51*51)
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2015-01-04 03:24
CalculusParametric EquationGeometric Construction
This example demonstrates the 3D visualization of Dini's Surface, precisely constructed from a grid of 51*51 points, showcasing its intricate spiral-like structure. Core mathematical concepts include surfaces, orthocenter, definite integrals, conic sections, and combinatorics. The construction utilizes GeoGebra commands and objects such as Sequence (to generate points), Join (to form a mesh), RemoveUndefined (to eliminate undefined objects), Textfield (for text display), Max/Min (to find extrema), and Surface (to create the 3D surface). Suitable for high school and above students to understand parametric surfaces, integral applications, and 3D geometric visualization.

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) → y1maxa
  12. Min(Y1E) → y1mina
  13. Max(Z1E) → z1maxa
  14. Min(Z1E) → z1mina
  15. Textfield(N) → inputBox6
  16. Surface(((5 * cos(u)) * sin(v)), ((r_Y * sin(u)) * sin(v)), (r_Z * (cos(v) + log(tan(v / 2)))) + (a * u), u, u_{min}, u_{max}, v, v_{min}, v_{max}) → h
  17. Textfield(h) → inputBox4

AI Drawing Prompt Reference

Visualize a detailed grid composed of 51x51 points to highlight its intricate spiral structure, and generate a 3D surface based on parametric equations formed by these points, showcasing a complex geometric shape in three-dimensional space with labeled key parameters and ranges.
The prompt above was compiled from the original drawing commands and is for reference only.