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Spiral on a Sphere

Spiral on a Sphere
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2022-01-25 18:22
Coordinate GeometrySolid GeometryParametric Equation
In collections Curves and Surfaces Curves and Spirals on Spheres
This example demonstrates a spiral on a sphere. It involves concepts of spherical geometry and parametric equations. Using the Surface and CurveCartesian commands, the spiral's trajectory can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Surface((cos(u) * sin(v)), (sin(u) * sin(v)), cos(v), u, 0, (2 * π), v, 0, π) → c
  2. CurveCartesian(cos(t) / sqrt(1 + (0.4^(2) * t^(2))), sin(t) / sqrt(1 + (0.4^(2) * t^(2))), (-(((0.4 * t)) / sqrt(1 + (0.4^(2) * t^(2))))), t, (-2 * π), (2 * π)) → a
  3. CurveCartesian(cos(t) / sqrt(1 + (0.3^(2) * t^(2))), sin(t) / sqrt(1 + (0.3^(2) * t^(2))), (-(((0.3 * t)) / sqrt(1 + (0.3^(2) * t^(2))))), t, (-2 * π), (2 * π)) → b
  4. Surface(((1 - u) * b(t)) + (u * a(t)), u, -1, 1, t, (-10 * π), (10 * π)) → d

AI Drawing Prompt Reference

Draw a spiral on the surface of a sphere. First, create a unit sphere. Then, draw two spirals on the sphere, with their radii decreasing as the angle increases. Finally, use these two spirals to generate a spiral surface, showing the dynamic change of the spiral on the sphere.
The prompt above was compiled from the original drawing commands and is for reference only.