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Hyperbolic Coaxial Family of Spheres

Hyperbolic Coaxial Family of Spheres
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2017-05-05 09:20
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric construction and properties of a hyperbolic coaxial family of spheres. Key math concepts include spheres, coaxial systems, hyperbolic geometry, and solid geometry. The construction uses GeoGebra commands and objects such as Point, Sphere, Intersect, PointIn, and Plane as outlined in the summary. Suitable for high school and above students to understand the construction methods of spherical geometry and coaxial systems.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Sphere(A, B) → a
  4. Sphere(B, A) → b
  5. Intersect(zAxis, yAxis) → C
  6. Point(xAxis) → D
  7. Sphere(C, D) → c
  8. Point(xAxis) → E
  9. PointIn(c) → F
  10. Sphere(E, F) → d
  11. Point(xAxis) → G
  12. Sphere(G, F) → e
  13. Intersect(yAxis, d, 1) → H
  14. Point(zAxis) → I
  15. Point(yAxis) → J
  16. Plane(H, I, J) → f