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Angle Sum and Area of Spherical Triangle

Angle Sum and Area of Spherical Triangle
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2017-09-04 06:54
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the angle sum and area calculation of spherical triangles. It involves core mathematical concepts such as spherical geometry, trigonometry, and area formulas. The construction uses GeoGebra commands like Sphere, PointIn, Intersect, CircleArc, Line, OrthogonalPlane, Plane, IntersectPath, Circle, and Angle. Suitable for high school students and math enthusiasts 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. Intersect(xAxis, zAxis) → D
  6. CircleArc(D, A, B) → c
  7. CircleArc(D, A, C) → d
  8. CircleArc(D, C, B) → e
  9. Line(D, A) → f
  10. Line(D, B) → g
  11. Line(D, C) → h
  12. OrthogonalPlane(A, f) → b
  13. Plane(C, f) → i
  14. Plane(B, f) → j
  15. IntersectPath(b, j) → k
  16. IntersectPath(i, b) → l
  17. Circle(A, 1, f) → p
  18. Intersect(l, p, 1) → E
  19. Intersect(k, p, 2) → F
  20. Angle(F, A, E) → α
  21. OrthogonalPlane(C, h) → m
  22. Plane(A, h) → n
  23. Plane(B, h) → o
  24. IntersectPath(n, m) → q
  25. IntersectPath(o, m) → r
  26. Circle(C, 1, h) → s
  27. Intersect(q, s, 1) → G
  28. Intersect(r, s, 1) → H
  29. Angle(H, C, G) → β
  30. OrthogonalPlane(B, g) → t
  31. Plane(A, g) → u
  32. Plane(C, g) → v
  33. IntersectPath(t, u) → f_1
  34. IntersectPath(v, t) → g_1
  35. Circle(B, 1, g) → c_1
  36. Intersect(f_1, c_1, 2) → I
  37. Intersect(g_1, c_1, 1) → J
  38. Angle(J, B, I) → γ
  39. Intersect(zAxis, a) → S, N
  40. Line(N, S) → h_1