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Part of a Sphere

Part of a Sphere
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2014-12-29 00:04
CircleSolid GeometryGeometric Construction
In collections surface 3D surface 3D
This example demonstrates a portion of a sphere. It involves concepts such as spheres, circles, straight lines, and reflections. Using GeoGebra commands like Sphere, PointIn, If, Segment, etc., a part of the sphere can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → a
  2. PointIn(a) → B
  3. PointIn(a) → A
  4. If(z(A) < 0, ((-(((Angle[A_0, (0, 0, 0), A, Plane[A, (0, 0, 0), A_0]] * 2) * π / 360)))) / °, (((Angle[A_0, (0, 0, 0), A, Plane[A, (0, 0, 0), A_0]] * 2) * π / 360)) / °) → aa1
  5. If(z(B) < 0, ((-(((Angle[B_0, (0, 0, 0), B, Plane[B, (0, 0, 0), B_0]] * 2) * π / 360)))) / °, (((Angle[B_0, (0, 0, 0), B, Plane[B, (0, 0, 0), B_0]] * 2) * π / 360)) / °) → ab1
  6. Segment(A_0, A) → c
  7. Segment(B_0, B) → d
  8. Min(aa1, ab1) → vb
  9. Max(aa1, ab1) → ve
  10. Segment(O, B) → h
  11. Surface((cos(u) * cos(v)), (sin(u) * cos(v)), sin(v), u, aa0, aa0 + ab0, v, vb, ve) → b
  12. Segment(A_0, O) → e
  13. Segment(B_0, O) → f
  14. Segment(O, A) → g
  15. Angle(A, O, A_0) → α
  16. Angle(B, O, B_0) → β
  17. Angle((x(A), y(A)), (0, 0), (x(B), y(B))) → γ
  18. Circle(zAxis, (1, 0, 0)) → k

AI Drawing Prompt Reference

Draw a part of a sphere with radius 1, including the center O, and points A and B on the sphere with z-coordinates less than 0. Construct a part of the sphere surface using points A and B, where angles α and β represent the angles between A and B with the center O, and γ is the angle between the projections of A and B on the xy-plane.
The prompt above was compiled from the original drawing commands and is for reference only.