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Spherical Lines: Angles Between Great Circles

Spherical Lines: Angles Between Great Circles
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2014-07-22 03:35
AngleCoordinate GeometrySolid Geometry
In collections Spherical Geometry Ideas
This example demonstrates how the angle between two great circles on a sphere can be measured by the angle between their poles. Key concepts include great circles and poles in spherical geometry. Commands used include Sphere, PointIn, Plane, IntersectPath, OrthogonalLine, Intersect, Angle, Line, OrthogonalPlane, and Point. Suitable for high school and above students studying spherical geometry.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → a
  2. PointIn(a) → A
  3. PointIn(a) → B
  4. PointIn(a) → C
  5. Plane(O, A, C) → b
  6. Plane(O, B, C) → c
  7. IntersectPath(c, a) → d
  8. IntersectPath(b, a) → e
  9. OrthogonalLine(O, c) → f
  10. OrthogonalLine(O, b) → g
  11. Intersect(f, a) → D, F
  12. Intersect(g, a) → E, G
  13. Angle(G, O, F) → α
  14. Line(O, C) → h
  15. OrthogonalPlane(C, h) → i
  16. IntersectPath(i, c) → j
  17. IntersectPath(b, c) → k
  18. IntersectPath(i, b) → l
  19. Point(j) → H
  20. Point(l) → I
  21. Angle(H, C, I) → γ

AI Drawing Prompt Reference

Draw a sphere and select three points A, B, and C on it. Draw two planes b and c through these points and the sphere's center O, and let them intersect the sphere to form paths d and e. Then, draw two lines f and g perpendicular to these planes from the center O, and let them intersect the sphere to form points D, E, F, and G. Measure the angle α formed by points F and G with the center O. Next, draw a line h from point C through the center O, and draw a plane i perpendicular to the plane containing point C, and let it intersect planes c and b to form points H and I, respectively. Measure the angle γ formed by points H and I with point C.
The prompt above was compiled from the original drawing commands and is for reference only.