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Sphere Parameterization

Sphere Parameterization
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2017-04-08 01:53
FunctionTrigonometrySolid GeometryParametric Equation
This example demonstrates how to plot a 3D sphere using parametric equations. Key math concepts include parametric equations, 3D geometry, and sphere properties. Construction highlights: the Surface command is used for the sphere, and CurveCartesian for the parametric curve, with objects a, mer, par, u representing the sphere, equator, curve, and parameter variable respectively. Suitable for high school and above students learning applications of parametric equations in spatial geometry.

GeoGebra Commands & Parameters

  1. Surface(((3 * cos(s)) * cos(t)), ((3 * sin(s)) * cos(t)), (3 * sin(t)), s, 0, (2 * π), t, 0, (2 * π)) → a
  2. CurveCartesian(a(s, π / 3), s, 0, (2 * π)) → mer
  3. CurveCartesian(a(π / 5, t), t, 0, (2 * π)) → par
  4. CurveCartesian(a((5 * t) - 2, (2 * t) + 3), t, (-10 * π), (20 * π)) → u