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Plane Equilateral Triangle & Sphere

Plane Equilateral Triangle & Sphere
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2019-06-15 18:51
TriangleCircleSolid Geometry
This example demonstrates the relationship between a plane equilateral triangle and a sphere. Key mathematical concepts include the properties of an equilateral triangle and the geometric features of a sphere. Using GeoGebra commands such as Point, Circle, Rotate, Segment, Polygon, and Sphere, an equilateral triangle is constructed and a sphere is built around it. Suitable for high school geometry and solid geometry courses.

GeoGebra Commands & Parameters

  1. Point(zAxis) → C
  2. Circle(C, b, zAxis) → e
  3. Point(e) → D
  4. Rotate(D, 120°, C, xOyPlane) → D'
  5. Circle(A, a) → c
  6. Point(c) → B
  7. Segment(D', B) → r
  8. Rotate(B, 120°, A) → B'
  9. Segment(D', B') → s
  10. Rotate(B', 120°, A) → B''
  11. Segment(D', B'') → q
  12. Segment(A, B) → f
  13. Angle(B, A, B') → α
  14. Segment(A, B') → g
  15. Angle(B', A, B'') → β
  16. Segment(A, B'') → h
  17. Polygon(B', B, B'') → t1, f2, f1, f3
  18. Sphere(A, a) → d
  19. Segment(A, C) → i
  20. Segment(D, B'') → m
  21. Segment(D, B) → n
  22. Segment(D, B') → p
  23. Segment(C, D) → j
  24. Angle(D, C, D', xOyPlane) → γ
  25. Segment(D', C) → k
  26. Rotate(D', 120°, C, xOyPlane) → D''
  27. Angle(D', C, D'', xOyPlane) → δ
  28. Segment(C, D'') → l
  29. Segment(D'', B) → t
  30. Segment(D'', B') → f_1
  31. Segment(D'', B'') → g_1
  32. Polygon(D, D'', D') → t2, d', d_1, d''