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Spherical Coordinates: Dynamic Illustration by Néstor Valles-Villarreal

Spherical Coordinates: Dynamic Illustration by Néstor Valles-Villarreal
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2019-04-15 10:42
TrigonometryCoordinate Geometry
This example illustrates dynamic transformations in spherical coordinates. Key mathematical concepts include spherical coordinates, transformations, and dynamic geometry. It uses commands such as Dilate (dilate), Segment (segment), Rotate (rotate), CircleSector (circle sector), CircleArc (circle arc), Plane (plane), and TextField (text field). Suitable for high school and above students to learn 3D geometric transformations 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