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Tessellating the Sphere: Trirectangular Spherical Triangle

Tessellating the Sphere: Trirectangular Spherical Triangle
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2014-07-03 09:45
TrigonometrySolid GeometryGeometric Construction
In collections Spherical Geometry Ideas
This example demonstrates how to tessellate a sphere using trirectangular spherical triangles. It involves core mathematical concepts such as spherical geometry, trigonometry, the cosine rule, and geometric transformations. Construction highlights include using GeoGebra commands like Sphere, PointIn, Mirror, Line, OrthogonalPlane, IntersectPath, Point, Circle, Plane, OrthogonalLine, and Intersect. Suitable for high school and above students to learn about spherical and spatial geometry construction.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → a
  2. PointIn(a) → A
  3. Mirror(a, O) → a'
  4. Mirror(A, O) → A'
  5. Line(A, O) → b
  6. OrthogonalPlane(O, b) → c
  7. IntersectPath(c, a) → d
  8. Point(d) → B
  9. Circle(A, B, A') → e
  10. Line(B, O) → f
  11. OrthogonalPlane(O, b) → g
  12. Plane(f, b) → h
  13. OrthogonalLine(O, h) → i
  14. Intersect(i, a, 2) → C
  15. Circle(A, C, A') → k

AI Drawing Prompt Reference

Tessellate a sphere using trirectangular spherical triangles by first drawing the sphere, then creating key points and lines through the center and points on the sphere using mirror and orthogonal operations, and finally completing the pattern with circles and intersections.
The prompt above was compiled from the original drawing commands and is for reference only.