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Rotating Arcs

Rotating Arcs
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2017-11-05 07:40
Solid GeometryTransformationGeometric Construction
This example demonstrates the generation of 3D shapes through rotating arcs. It involves core mathematical concepts like line segments, spheres, rotations, and circular arcs. Key GeoGebra commands and objects used in the construction include Intersect, Sphere, Rotate, and CircleArc. Suitable for high school and above students studying solid geometry and spatial transformations.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → A
  2. Sphere(A, 1) → a
  3. Intersect(zAxis, a) → B, C
  4. Intersect(xAxis, a) → D, E
  5. Intersect(yAxis, a) → F, G
  6. Rotate(E, (-(45°)), yAxis) → E'
  7. Rotate(E, 45°, yAxis) → E'_1
  8. CircleArc(A, E'_1, E') → c
  9. Rotate(c, α, xAxis) → c'
  10. Rotate(c', (-(90°)), yAxis) → c''
  11. Rotate(c', 90°, yAxis) → c''_1
  12. Rotate(c', (-(180°)), yAxis) → c''_2
  13. Rotate(c', 90°, zAxis) → c''_3
  14. Rotate(c', (-(90°)), zAxis) → c''_4
  15. Rotate(c', 90°, xAxis) → c''_5
  16. Rotate(c'', 90°, zAxis) → c'''
  17. Rotate(c''_4, (-(90°)), yAxis) → d
  18. Rotate(c''_3, 90°, yAxis) → e
  19. Rotate(c''_2, (-(90°)), xAxis) → f
  20. Rotate(c''_1, (-(90°)), zAxis) → g