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Spherical Triangle Construction and Properties

Spherical Triangle Construction and Properties
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2017-11-23 16:04
TriangleAngleSolid GeometryGeometric Construction
In collections Spherical figures
This example demonstrates the construction of a spherical triangle on a sphere surface. Key mathematical concepts include spherical geometry, great circle arcs, plane intersections, and spherical angles. The construction utilizes GeoGebra commands such as Sphere, PointIn, CircleArc, Segment, Plane, OrthogonalPlane, IntersectPath, and Angle to define vertices and edges dynamically. It is suitable for high school or university students studying solid geometry and spherical trigonometry.

GeoGebra Commands & Parameters

  1. Sphere(O, P) → a
  2. PointIn(a) → A
  3. PointIn(a) → B
  4. PointIn(a) → C
  5. CircleArc(O, A, B) → c
  6. CircleArc(O, B, C) → d
  7. CircleArc(O, C, A) → e
  8. Segment(O, A) → f
  9. Segment(O, B) → g
  10. Segment(O, C) → h
  11. Plane(O, A, B) → b
  12. OrthogonalPlane(A, f) → i
  13. IntersectPath(b, i) → j
  14. Plane(O, A, C) → k
  15. IntersectPath(k, i) → l
  16. Angle(j, l) → α
  17. OrthogonalPlane(B, g) → m
  18. IntersectPath(m, b) → n
  19. Plane(O, B, C) → o
  20. IntersectPath(o, m) → p
  21. Angle(p, n) → β
  22. OrthogonalPlane(C, h) → q
  23. IntersectPath(k, q) → r
  24. IntersectPath(q, o) → s
  25. Point(r) → D
  26. Point(s) → E
  27. Angle(D, C, E) → γ