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Animated Multiple Spheres 3D

Animated Multiple Spheres 3D
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2019-05-12 22:50
TrigonometrySolid GeometryComplex NumberGraphing
This example demonstrates the motion and transformation of multiple spheres in 3D space through animation. The core mathematical concepts involved include solid geometry, trigonometry, and complex numbers. The construction utilizes GeoGebra commands and objects such as Surface, Rotate, Mirror, Dilate, and CurveCartesian. It is suitable for high school and above students to learn and understand spatial geometry, transformations, and data analysis.

GeoGebra Commands & Parameters

  1. Surface(((0.75 * sin(u)) * cos(v)), ((0.75 * sin(u)) * sin(v)), (0.75 * (a / π + cos(u) - 2.5)), u, 0, π, v, 0, (2 * π)) → green1
  2. Surface(((0.75 * sin(u)) * cos(v)), ((0.75 * sin(u)) * sin(v)), (0.75 * (((-a)) / π + cos(u) + 3)), u, 0, π, v, 0, (2 * π)) → red1
  3. Rotate(green1, a, yAxis) → green2
  4. Mirror(green1, B) → blue
  5. Rotate(red1, (-a), yAxis) → red3
  6. Mirror(xOyPlane, B) → e
  7. Rotate(xAxis, a, yAxis) → xAxis'
  8. Rotate(red1, (-a), xAxis') → red2
  9. Rotate(green1, a, xAxis') → green3
  10. Dilate(blue, sin(abs(a) / π), B) → blue'
  11. Surface(((0.75 * sin(u)) * cos(v)), ((0.75 * sin(u)) * sin(v)), (0.75 * (a / π + cos(u) - 2.5)), u, 0, π, v, 0, (2 * π)) → b
  12. Surface(((0.75 * sin(u)) * cos(v)), ((0.75 * sin(u)) * sin(v)), (0.75 * cos(u)), u, 0, π, v, 0, (2 * π)) → center
  13. CurveCartesian(cos((a * n)), sin((a * n)), n, n, 0, (2 * π)) → g
  14. Surface(((0.75 * sin(u)) * cos(v)), ((0.75 * sin(u)) * sin(v)), (a * cos(u)), u, 0, π, v, 0, (2 * π)) → i

AI Drawing Prompt Reference

Create a 3D animated scene with multiple spheres and their transformations. A central sphere of radius 0.75 moves vertically along the z-axis with parameter a. Two additional spheres, one green and one red, are offset upward and downward respectively, and rotate around the y-axis. The green sphere is mirrored about a point to form a blue sphere, which then scales according to a sine function. A 3D spiral curve winds around the z-axis, and a surface deforms with a. All objects animate continuously with parameter a, showing rotation, mirroring, scaling, and translation of spheres.
The prompt above was compiled from the original drawing commands and is for reference only.