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Triangles on a Sphere

Triangles on a Sphere
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2019-06-15 10:41
TriangleVectorSolid Geometry
This example demonstrates triangles on a sphere. Key mathematical concepts include properties of spherical triangles, vectors, and angles. Using GeoGebra commands such as Sphere, PointIn, IntersectPath, etc., one can construct spherical triangles. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → a
  2. PointIn(a) → A
  3. PointIn(a) → B
  4. PointIn(a) → C
  5. IntersectPath(Plane[A, B, (0, 0, 0)], a) → c
  6. IntersectPath(Plane[A, C, (0, 0, 0)], a) → d
  7. IntersectPath(Plane[B, C, (0, 0, 0)], a) → e
  8. UnitVector(Tangent[A, c]) → vAB
  9. UnitVector(Tangent[A, d]) → vAC
  10. UnitVector(Tangent[B, e]) → vBC
  11. Vector(B, B - UnitVector[Tangent[B, c]]) → vBA
  12. Vector(C, C - UnitVector[Tangent[C, d]]) → vCA
  13. Vector(C, C - UnitVector[Tangent[C, e]]) → vCB
  14. Angle(vAB, vAC) → α
  15. Angle(vBC, vBA) → β
  16. Angle(vCA, vCB) → γ
  17. LaTeX(α, true, true) → text1
  18. Point(c) → D
  19. CircumcircleArc(A, D, B) → f
  20. Point(e) → E
  21. CircumcircleArc(B, E, C) → g
  22. Point(d) → F
  23. CircumcircleArc(C, F, A) → h