MathPlotAI Logo MathPlotAI

Wrap a Function on the Sphere

Wrap a Function on the Sphere
Loading the math board and drawing, please wait…
2020-03-16 15:27
FunctionCoordinate GeometrySolid GeometryGraphing
This example demonstrates how to wrap a function around a sphere, creating a 3D function graph in space. Key math concepts include functions, sphere, coordinate geometry, and transformations. It uses GeoGebra commands like CurveCartesian, Sphere, Mirror, and Textfield. Suitable for high school and above students exploring the intersection of spatial geometry and function graphs.

GeoGebra Commands & Parameters

  1. CurveCartesian(x(O) + (2 * u / (1 + u^(2) + f(u)^(2))), y(O) + (2 * f(u) / (1 + u^(2) + f(u)^(2))), z(O) + (-1 + u^(2) + f(u)^(2)) / (1 + u^(2) + f(u)^(2)), u, -10, 10) → a_1
  2. Sphere(O, 1) → b_1
  3. CurveCartesian(((2 * u / (1 + u^(2) + f(u)^(2))), y(O) - (2 * f(u) / (1 + u^(2) + f(u)^(2))), z(O) + (-1 + u^(2) + f(u)^(2)) / (1 + u^(2) + f(u)^(2))), u, -10, 10) → d
  4. Mirror(a_1, O) → e
  5. Mirror(d, O) → d'
  6. CurveCartesian(x(O) + (2 * u / (1 + u^(2) + f(u)^(2))), y(O) + (-1 + u^(2) + f(u)^(2)) / (1 + u^(2) + f(u)^(2)), z(O) + (2 * f(u) / (1 + u^(2) + f(u)^(2))), u, -10, 10) → g
  7. CurveCartesian(x(O) + (2 * u / (1 + u^(2) + f(u)^(2))), y(O) + (-1 + u^(2) + f(u)^(2)) / (1 + u^(2) + f(u)^(2)), z(O) - (2 * f(u) / (1 + u^(2) + f(u)^(2))), u, -10, 10) → h
  8. Mirror(g, O) → g'
  9. Mirror(h, O) → h'
  10. CurveCartesian(x(O) + (-1 + u^(2) + f(u)^(2)) / (1 + u^(2) + f(u)^(2)), y(O) + (2 * u / (1 + u^(2) + f(u)^(2))), z(O) - (2 * f(u) / (1 + u^(2) + f(u)^(2))), u, -10, 10) → i
  11. CurveCartesian(x(O) + (-1 + u^(2) + f(u)^(2)) / (1 + u^(2) + f(u)^(2)), y(O) + (2 * u / (1 + u^(2) + f(u)^(2))), z(O) + (2 * f(u) / (1 + u^(2) + f(u)^(2))), u, -10, 10) → j
  12. Mirror(j, O) → j'
  13. Mirror(i, O) → i'
  14. Textfield(f) → ChampTexte1