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Spherical Coordinates: Dynamic Illustration

Spherical Coordinates: Dynamic Illustration
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2017-12-29 06:29
Coordinate GeometrySolid GeometryTransformation
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources Plotting Points Multivariable Calculus
This example demonstrates dynamic transformations in spherical coordinates. Key mathematical concepts include spherical coordinates, transformations, and dynamic geometry. Using commands like Dilate, Segment, and Rotate, the example allows for interactive adjustments of points and shapes in spherical coordinates. Suitable for high school and above students studying solid and dynamic geometry.

GeoGebra Commands & Parameters

  1. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], B) → A'
  2. Segment(A, A') → f
  3. Rotate(B, If[2 < e ≤ 3, ((e - 2) * b), b], A) → B'
  4. Segment(A, B') → g
  5. CircleSector(A, B, B') → h
  6. Rotate(A, If[1 < e ≤ 2, ((e - 1) * π / 2), π / 2], A, Line[(0, 0, 0), (0, 1, 0)]) → A'_2
  7. Rotate(A', If[1 < e ≤ 2, ((-(e - 1)) * π / 2), ((-π)) / 2], A, Line[(0, 0, 0), (0, 1, 0)]) → A''
  8. Segment(A'_2, A'') → f'
  9. Rotate(A'', If[3 < e ≤ 4, ((-(e - 3)) * π), (-π)], A, Plane[A'', A, B']) → A'''_1
  10. CircleArc(A, A'', A'''_1) → k
  11. CircleArc(A, (0, 0, a), (0, 0, (-a)), Plane[A, B', (0, 0, (-a))]) → p
  12. Rotate(A'', If[4 < e ≤ 5, ((-(e - 4)) * c), (-c)], A, Plane[A'', A, B']) → A'''
  13. CircleArc(A, A''', A'''_1) → r
  14. CircleSector(A, A''', A'') → q
  15. Plane((0, 0, 0), (1, 0, 0), (0, 1, 0)) → i
  16. Textfield(a) → InputBox1
  17. Textfield(b) → InputBox2
  18. Textfield(c) → InputBox3

AI Drawing Prompt Reference

Create a dynamic illustration of transformations in spherical coordinates, showing a point moving along a spherical trajectory, with multiple auxiliary lines and sector regions generated through dilation, rotation, and translation, demonstrating the dynamic changes of points in spherical coordinates, ultimately forming a polygonal structure with arcs and sectors that highlights the effects of spatial geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.