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Sphere Animations Demo

Sphere Animations Demo
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2016-12-27 00:49
SequenceCoordinate GeometrySolid Geometry
This example demonstrates sphere movements and transformations through animations. It involves core math concepts like solid geometry, sequences, random variables, and coordinate geometry. Construction highlights include using GeoGebra commands like Sequence, Max, Slider Animation, and Locus. Suitable for high school students and math enthusiasts exploring spatial geometry and dynamic changes.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Dilate[(i, j, (h * f(sqrt(i^(2) + j^(2))))), c + f(sqrt(i^(2) + j^(2)))], i, (-2 * π), (2 * π), (4 * π / n)], j, (-2 * π), (2 * π), (4 * π / n)) → liste1
  2. Sequence(Sequence[Sphere[Element[liste1, j, i], (1 / 2 * Min[{Distance[Element[liste1, j, i], Element[liste1, j, i + 1]], Distance[Element[liste1, j, i], Element[liste1, j, i - 1]], Distance[Element[liste1, j, i], Element[liste1, j + 1, i]], Distance[Element[liste1, j, i], Element[liste1, j - 1, i]]}])], i, 2, n, 2], j, 2, n, 2) → liste3
  3. Sequence(Sequence[Sphere[Element[liste1, j, i], (1 / 2 * Min[{Distance[Element[liste1, j, i], Element[liste1, j, i + 1]], Distance[Element[liste1, j, i], Element[liste1, j, i - 1]], Distance[Element[liste1, j, i], Element[liste1, j + 1, i]], Distance[Element[liste1, j, i], Element[liste1, j - 1, i]]}])], i, 3, n, 2], j, 3, n, 2) → liste4
  4. Sequence(Sequence[Sphere[Element[liste1, j, i], (1 / 2 * Min[{Distance[Element[liste1, j, i], Element[liste1, j, i + 1]], Distance[Element[liste1, j, i], Element[liste1, j, i - 1]], Distance[Element[liste1, j, i], Element[liste1, j + 1, i]], Distance[Element[liste1, j, i], Element[liste1, j - 1, i]]}])], i, 3, n, 2], j, 2, n, 2) → liste5
  5. Sequence(Sequence[Sphere[Element[liste1, j, i], (1 / 2 * Min[{Distance[Element[liste1, j, i], Element[liste1, j, i + 1]], Distance[Element[liste1, j, i], Element[liste1, j, i - 1]], Distance[Element[liste1, j, i], Element[liste1, j + 1, i]], Distance[Element[liste1, j, i], Element[liste1, j - 1, i]]}])], i, 2, n, 2], j, 3, n, 2) → liste6
  6. Max(z(Element[liste1, floor(n / 2) + 1, floor(n / 2) + 1]), 15) → d

AI Drawing Prompt Reference

Create a sphere animation demonstration with a series of scaled spheres. First, generate a series of spheres rotating around the origin, with each sphere's position determined by its coordinates. Then, determine the radius of each sphere based on the distances to its neighboring spheres. Finally, generate a series of new spheres based on these positions and radii, forming a dynamic sequence of spheres.
The prompt above was compiled from the original drawing commands and is for reference only.