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Deriving a Sphere

Deriving a Sphere
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2015-11-18 12:24
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to derive a sphere through geometric construction. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Intersect, Sphere, and PointIn, a spherical model can be constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → A
  2. Sphere(A, 2) → a
  3. PointIn(a) → P
  4. Line(P, xAxis) → b
  5. Line(P, yAxis) → c
  6. Line(P, zAxis) → d
  7. Mirror(P, xOyPlane) → P'
  8. Plane(yAxis, xAxis) → e
  9. Mirror(P, e) → P'_1
  10. Midpoint(P, P'_1) → B
  11. OrthogonalLine(B, xAxis, space) → f
  12. Intersect(f, xAxis) → E
  13. Polygon(A, B, E) → poly1, e_1, a_1, b_1
  14. Polygon(A, P, B) → poly2, b_2, a_2, p
  15. Segment(A, P) → r
  16. Midpoint(r) → F
  17. Midpoint(a_2) → G
  18. Midpoint(p) → H
  19. Midpoint(b_1) → I
  20. Midpoint(a_1) → J