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Drawing Curves on a Sphere

Drawing Curves on a Sphere
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2016-01-24 21:39
Coordinate GeometrySolid GeometryParametric Equation
This example demonstrates how to draw curves on a sphere. Key mathematical concepts include spherical geometry and parametric equations. Using commands like CurveCartesian, Sphere, and Surface, complex geometric shapes can be constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. CurveCartesian(((-t) * cos(((c * π) * sin(t - d2)))), (t * sin(((c * π) * sin(t - d2)))), t, 0, (2 * π)) → b
  2. CurveCartesian((t * sin(((c * π) * sin(t - d1)))), (t * cos(((c * π) * sin(t - d1)))), t, 0, (2 * π)) → a
  3. Sphere((0, 0, 0), (2 * π)) → d_1
  4. CurveCartesian((t * sin(((c * π) * sin(t - d1)))), (t * cos(((c * π) * sin(t - d1)))), sqrt(((2 * π))^(2) - t^(2)), t, 0, (2 * π)) → e
  5. CurveCartesian(((-t) * cos(((c * π) * sin(t - d2)))), (t * sin(((c * π) * sin(t - d2)))), sqrt(((2 * π))^(2) - t^(2)), t, 0, (2 * π)) → f
  6. CurveCartesian((tt * cos(((π / 2 - ((c * π) * sin(tt - d1))) * (1 - t)) + (t * (π - ((c * π) * sin(tt - d2)))))), (tt * sin(((π / 2 - ((c * π) * sin(tt - d1))) * (1 - t)) + (t * (π - ((c * π) * sin(tt - d2)))))), sqrt(((2 * π))^(2) - tt^(2)), t, 0, 1) → i
  7. CurveCartesian((tt * cos(((π / 2 - ((c * π) * sin(tt - d1))) * (1 - t)) + (t * (π - ((c * π) * sin(tt - d2)))))), (tt * sin(((π / 2 - ((c * π) * sin(tt - d1))) * (1 - t)) + (t * (π - ((c * π) * sin(tt - d2)))))), t, 0, 1) → j
  8. Surface((tt * cos(((π / 2 - ((c * π) * sin(tt - d1))) * (1 - t)) + (t * (π - ((c * π) * sin(tt - d2)))))), (tt * sin(((π / 2 - ((c * π) * sin(tt - d1))) * (1 - t)) + (t * (π - ((c * π) * sin(tt - d2)))))), sqrt(((2 * π))^(2) - tt^(2)), t, 0, 1, tt, 0, (2 * π)) → k