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Fly's Flight Curve

Fly's Flight Curve
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2020-12-14 20:43
FunctionCoordinate GeometryParametric Equation
This example demonstrates the trajectory curve of a fly's flight. Key mathematical concepts include parametric curves and similarity transformations. Using GeoGebra commands such as Surface, Sequence, and CurveCartesian, the dynamic flight path of the fly can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and parametric equations.

GeoGebra Commands & Parameters

  1. Surface(((2 + cos(t)) * cos(u)), ((2 + cos(t)) * sin(u)), sin(t), t, 0, (2 * π), u, 0, (2 * π)) → a
  2. Sequence(CurveCartesian[((2 + cos(t)) * cos(u)), ((2 + cos(t)) * sin(u)), sin(t), u, 0, (2 * π)], t, 0 + (p * n), (2 * π) + (p * n), π / 10) → L_2
  3. Sequence(CurveCartesian[((2 + cos(t)) * cos(u)), ((2 + cos(t)) * sin(u)), sin(t), t, 0, (2 * π)], u, 0 + (q * n), (2 * π) + (q * n), π / 10) → L_1
  4. CurveCartesian(((2 + cos((p * u))) * cos((q * u))), ((2 + cos((p * u))) * sin((q * u))), sin((p * u)), u, 0, n) → b
  5. Line(C, A) → f
  6. Circle(B, 0.5, f) → c
  7. Point(c) → D
  8. Rotate(D, k, f) → D'
  9. Polygon(B, D', C) → t1, c_1, b_1, d'
  10. Mirror(D, f) → D'_{1}
  11. Rotate(D'_{1}, (-k), f) → E
  12. Polygon(B, E, C) → t2, c_2, b_2, e
  13. Circle(C, 0.35, f) → d
  14. Point(d) → G
  15. Rotate(G, k, f) → G'
  16. Mirror(G, f) → G'_{1}
  17. Rotate(G'_{1}, (-k), f) → H
  18. Polygon(B, G', C) → t3, c_3, b_3, g'
  19. Polygon(B, G'_{1}, C) → t4, c_4, b_4, g'_{1}

AI Drawing Prompt Reference

Create a fly's flight curve demonstrating parametric curves and similarity transformations. Start by generating a 3D surface, then use sequence commands to create multiple curves rotating around different axes to form a dynamic flight path. Apply mirror and rotation operations to generate several polygons and circles, symmetrically distributed around a central point, resulting in a complex and symmetric representation of the fly's trajectory.
The prompt above was compiled from the original drawing commands and is for reference only.