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Surface on Sphere

Surface on Sphere
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2015-04-21 00:31
FunctionCoordinate GeometrySolid Geometry
In collections surface 3D surface 3D My 3D Collection
This example demonstrates a surface on a sphere. It involves spherical geometry and surface construction. By using commands like CurveCartesian, Sequence, and Surface, you can dynamically adjust the surface parameters and observe how the surface changes on the sphere. Suitable for high school mathematics education and students learning solid geometry.

GeoGebra Commands & Parameters

  1. CurveCartesian((cos((a * t)) * cos((b * t))), (sin((a * t)) * cos((b * t))), sin((b * t)), t, 0, ((tm * 2) * π)) → c_1
  2. CurveCartesian((cos((c * t)) * cos((d * t))), (sin((c * t)) * cos((d * t))), sin((d * t)), t, 0, ((tm * 2) * π)) → c_2
  3. Sequence(Segment[((cos((a * t)) * cos((b * t))), (sin((a * t)) * cos((b * t))), sin((b * t))), ((cos((c * t)) * cos((d * t))), (sin((c * t)) * cos((d * t))), sin((d * t)))], t, (2 * π / n), ((tm * 2) * π), (2 * π / n)) → liste1
  4. Sequence(Segment[Point[c_1, i], Point[c_2, 1 - i]], i, 1 / n, 1, 1 / ((tm * n))) → liste2
  5. Surface(((v * cos((a * u))) * cos((b * u))) + (((1 - v) * cos((c * u))) * cos((d * u))), ((v * sin((a * u))) * cos((b * u))) + (((1 - v) * sin((c * u))) * cos((d * u))), (v * sin((b * u))) + ((1 - v) * sin((d * u))), u, 0, ((tm * 2) * π), v, 0, 1) → f
  6. Surface(((v * cos((a * u))) * cos((b * u))) + (((1 - v) * cos((c * (((tm * 2) * π) - u)))) * cos((d * (((tm * 2) * π) - u)))), ((v * sin((a * u))) * cos((b * u))) + (((1 - v) * sin((c * (((tm * 2) * π) - u)))) * cos((d * (((tm * 2) * π) - u)))), (v * sin((b * u))) + ((1 - v) * sin((d * (((tm * 2) * π) - u)))), u, 0, ((tm * 2) * π), v, 0, 1) → e