MathPlotAI Logo MathPlotAI

Intersection of Spheres

Intersection of Spheres
Loading the math board and drawing, please wait…
2015-04-15 20:32
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the intersection of spheres or the union of portions of spheres. The core mathematical concepts involved are solid geometry, specifically spheres and spherical surfaces. Using commands such as Circle, Intersect, Sphere, IntersectConic, If, and Surface, the intersection of spheres or the union of spherical portions can be constructed. Suitable for high school or university-level solid geometry studies.

GeoGebra Commands & Parameters

  1. Circle((0, 0), rb) → cb
  2. Circle((0, h), ra) → ca
  3. Intersect(ca, cb) → I_1, I_2, ,
  4. Sphere((0, 0, (-y(I_1))), rb) → sb
  5. Sphere((0, 0, h - y(I_1)), ra) → sa
  6. IntersectConic(sa, sb) → e
  7. If(Defined[e], Angle[(0, 0, -10), (0, 0, (-y(I_1))), Point[e, 0]], 1.5708) → β
  8. If(Defined[e], Angle[(0, 0, -20), (0, 0, h - y(I_1)), Point[e, 0]], 0) → α
  9. Surface(((ra * cos(u)) * cos(v)), ((ra * sin(u)) * cos(v)), h - y(I_1) + (ra * sin(v)), u, 0, 6.28319, v, -1.5708, ((-π)) / 2 + α) → a
  10. Surface(((rb * cos(u)) * cos(v)), ((rb * sin(u)) * cos(v)), (-y(I_1)) + (rb * sin(v)), u, 0, 6.28319, v, ((-π)) / 2 + β, 1.5708) → b
  11. Surface(((rb * cos(u)) * cos(v)), ((rb * sin(u)) * cos(v)), (-y(I_1)) + (rb * sin(v)), u, 0, 6.28319, v, ((-π)) / 2 + β, 1.5208) → bbb
  12. Surface(((rb * cos(u)) * cos(v)), ((rb * sin(u)) * cos(v)), (-y(I_1)) + (rb * sin(v)), u, 0, 6.29, v, ((-π)) / 2 + β, 1.5208) → bb
  13. Surface(((ra * cos(u)) * cos(v)), ((ra * sin(u)) * cos(v)), h - y(I_1) + (ra * sin(v)), u, 0, 6.28319, v, -1.58, ((-π)) / 2 + α) → aa
  14. Surface(((ra * cos(u)) * cos(v)), ((ra * sin(u)) * cos(v)), h - y(I_1) + (ra * sin(v)), u, 0, 6.28, v, -1.5708, ((-π)) / 2 + α) → aaa