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Dynamic Colors: Sphere Covered With Colored Tracing Curves

Dynamic Colors: Sphere Covered With Colored Tracing Curves
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2019-05-28 11:50
TrigonometrySolid GeometryParametric EquationGraphing
This example demonstrates a dynamic visualization of a sphere covered with colored tracing curves. Key math concepts include sphere, rotation, tangent function, parametric curves, and locus. Construction highlights from the summary involve GeoGebra commands/objects like CurveCartesian, Point, Rotate, Line, and Circle. Suitable for high school and above students studying solid geometry, parametric equations, and dynamic geometry, or for educational demonstrations.

GeoGebra Commands & Parameters

  1. CurveCartesian((sin(a) * cos(a / 2)), (sin(a) * sin(a / 2)), cos(a), a, 0, (4 * π)) → b
  2. Point(b) → C
  3. Rotate(b, arg(C), zAxis) → c
  4. Point(zAxis) → B
  5. Line(B, A) → f
  6. Circle(f, C) → d