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Parasol Surfaces

Parasol Surfaces
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2020-07-01 15:27
Solid GeometryCalculusProbability & Statistics
This example demonstrates the 3D geometric shape of parasol surfaces and their variation patterns. It involves core mathematical concepts such as surfaces, hypergeometric distribution, frequency distribution, means, calculus, and planes. The construction uses commands like Surface and Segment, along with objects like m, n_2, n_3, n_1, f, O, R, nn, A, g, B, C, c, h, d, D, E, p, e, q, i, Color. It is suitable for high school and above students learning solid geometry, calculus, and probability & statistics.

GeoGebra Commands & Parameters

  1. Surface(x(A) + (((g(i) * R) * cos(i)) * cos(j)), y(A) + (((g(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, 0, 6.28319, j, 0, π) → c
  2. Surface(x(C) + (((h(i) * R) * cos(i)) * cos(j)), y(C) + (((h(i) * R) * sin(i)) * cos(j)), z(C) + (R * sin(j)) + 2, i, 0, 6.28319, j, 0, π) → d
  3. Surface(x(D) + (((p(i) * R) * cos(i)) * cos(j)), y(D) + (((p(i) * R) * sin(i)) * cos(j)), z(D) + (R * sin(j)) + 2, i, 0.1, 6.283, j, 0.1, π) → e
  4. Surface(x(E) + (((q(i) * R) * cos(i)) * cos(j)), y(E) + (((q(i) * R) * sin(i)) * cos(j)), z(E) + (R * sin(j)) + 2, i, 0.1, 6.283, j, 0.1, π) → i
  5. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A1, A2, j, 0, π) → B1
  6. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A2, A3, j, 0, π) → B2
  7. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A3, A4, j, 0, π) → B3
  8. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A4, A5, j, 0, π) → B4
  9. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A5, A6, j, 0, π) → B5
  10. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A6, A7, j, 0, π) → B6
  11. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A7, A8, j, 0, π) → B7
  12. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A8, A9, j, 0, π) → B8
  13. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A9, A10, j, 0, π) → B9
  14. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A10, A11, j, 0, π) → B10
  15. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A11, A12, j, 0, π) → B11
  16. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A12, A13, j, 0, π) → B12
  17. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A13, A14, j, 0, π) → B13
  18. Segment(O, O + (0, 0, 2)) → j
  19. Segment(A, A + (0, 0, 3.5)) → k
  20. Segment(D, D + (0, 0, 3.5)) → l
  21. Segment(E, E + (0, 0, 3.5)) → n
  22. Segment(C, C + (0, 0, 3.5)) → r

AI Drawing Prompt Reference

Draw a set of 3D parasol surfaces to demonstrate their variation patterns. These surfaces are generated by parametric equations, rotating around a central axis with height varying by angle, forming an umbrella-like structure. Surfaces differ by parameters to create a layered effect, resulting in a complex geometric form. Start with a central reference surface, then generate multiple concentric surfaces around the central axis, and finally add several vertical line segments to enhance the sense of depth.
The prompt above was compiled from the original drawing commands and is for reference only.