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Regular Polygons on a Sphere

Regular Polygons on a Sphere
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2018-05-04 22:32
PolygonTrigonometrySolid Geometry
This example demonstrates how to construct regular polygons on a sphere using GeoGebra commands such as Sphere, PointIn, Line, OrthogonalPlane, IntersectPath, Plane, Angle, and Polygon. It involves spherical geometry and trigonometry. Suitable for high school math education and students learning spherical geometry.

GeoGebra Commands & Parameters

  1. Sphere(A, B) → a
  2. PointIn(a) → C
  3. PointIn(a) → D
  4. Line(A, D) → f
  5. OrthogonalPlane(C, f) → b
  6. IntersectPath(b, a) → c
  7. Sequence(Rotate[C, ((k * 2) * π / n), f], k, 0, n) → punts
  8. Sequence(CircleArc[A, punts(k), punts(k + 1)], k, 1, n) → polr
  9. Plane(A, punts(2), punts(3)) → e
  10. Plane(A, punts(3), punts(4)) → g
  11. Angle(g, e) → β
  12. Plane(A, D, punts(1)) → d
  13. Plane(A, D, punts(2)) → h
  14. Angle(d, h) → γ
  15. IntersectPath(e, g) → i
  16. Plane(punts(1), punts(2), punts(3)) → j
  17. Polygon(C, punts(2), n, j) → pol1, k, h_1, i_1, j_1, k_1, l_1, m_1, E, F, G, H, l, I, J, K, L, M, N, O, P, Q, m, p, q, r, s, f_1, g_1
  18. IntersectPath(h, d) → n_1
  19. Sequence(Triangleesfèric[A, B, D, punts(k + 1), punts(k)], k, 1, n) → lli_1