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Rotation of Spheres and Rainbow Rings

Rotation of Spheres and Rainbow Rings
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2022-06-28 12:41
TrigonometryCoordinate GeometrySolid Geometry
This example demonstrates the phenomenon of rainbow rings generated during the rotation of spheres. It involves core mathematical concepts such as sphere geometry, rotational transformations, stochastic processes, and locus. The construction utilizes GeoGebra commands like Circle, Zip, Rotate, CurveCartesian, and Element. Suitable for high school students and math enthusiasts studying solid geometry and transformation applications.

GeoGebra Commands & Parameters

  1. Circle((x(w), y(w), z(w)), 1, Vector[(0, 1, 0)]) → d
  2. Zip(Rotate[Circle[(x(w), y(w), z(w)), g(rot, t), Vector[(0, 1, 0)]], ((2 * rot) * π / max)], rot, Lm) → LC
  3. Rotate(Translate[Sphere[(0, 0, 0), 1.7], w], t / 4) → s
  4. CurveCartesian((cos((4 * θ)) + 3; θ), θ, 0, (2 * π)) → b
  5. Zip(Rotate[s, ((2 * rot) * π / 4)], rot, Ln) → LS
  6. Element(LC, A1) → B1
  7. Element(LC, A2) → B2
  8. Element(LC, A3) → B3
  9. Element(LC, A4) → B4
  10. Element(LC, A5) → B5
  11. Element(LC, A6) → B6
  12. Element(LC, A7) → B7
  13. Element(LC, A8) → B8
  14. Element(LC, A9) → B9
  15. Element(LC, A10) → B10
  16. Element(LC, A11) → B11
  17. Element(LC, A12) → B12
  18. Element(LC, A13) → B13
  19. Element(LC, A14) → B14
  20. Element(LC, A15) → B15
  21. Element(LC, A16) → B16
  22. Element(LC, A17) → B17
  23. Element(LC, A18) → B18
  24. Element(LC, A19) → B19
  25. Element(LC, A20) → B20
  26. Element(LC, A21) → B21
  27. Element(LC, A22) → B22
  28. Element(LC, A23) → B23
  29. Element(LC, A24) → B24

AI Drawing Prompt Reference

Draw a rotating sphere with colorful rainbow rings generated on its surface. The sphere rotates around a vertical axis, creating a stochastic pattern of colored rings. Start by drawing the sphere, then use rotations and transformations to generate the rings, which consist of multiple points forming a random distribution of colorful paths. Finally, combine the sphere and the rings to visualize the mathematical relationship between rotation and the rainbow effect.
The prompt above was compiled from the original drawing commands and is for reference only.