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Second Egg to Pick Up

Second Egg to Pick Up
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2020-04-12 15:58
SequenceCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the dynamic generation of spherical surfaces and sequenced surfaces in three-dimensional space. It involves core mathematical concepts such as solid geometry, sequences, coordinate geometry, and geometric construction. Key GeoGebra commands and objects used include Sphere, Surface, and Sequence. Suitable for high school and above students exploring spatial geometry and parametric surfaces.

GeoGebra Commands & Parameters

  1. Sphere((0, 0), 1) → a
  2. Surface((cos(k) * cos(a + sin((5 * k)))), (cos(k) * sin(a + sin((5 * k)))), (h * sin(k)), k, ((-π)) / 2, π / 2, a, 0, (ep * π / n)) → C1
  3. Sequence(Rotate[C1, i, zAxis], i, 0, (2 * π), (2 * π / n)) → l1
  4. Surface((cos(k) * cos(a + sin((5 * k)))), sin(k), (cos(k) * sin(a + sin((5 * k)))), k, ((-π)) / 2, π / 2, a, 0, (ep * π / n)) → b
  5. Surface(((1.02 * cos(k)) * cos(a)), (((1.02 * sin(k)) * cos(a)) * sin(k)), (h * sin(a)), k, 0, (2 * π), a, 0, (2 * π)) → c
  6. Surface(((0.99 * cos(i)) * cos(j)), ((0.99 * cos(i)) * sin(j)), (h * sin(i)), i, 0, (2 * π), j, 0, (2 * π)) → d