Intersection of two spheres
This activity belongs to the GeoGebra book Linkages.
The degrees of freedom of a configuration can vary in particular cases. Let's look at a simple example.
Let there be 4 points C, D, E and F that are one unit away from two points A and B. We will assume that point A remains fixed at the origin of coordinates, while point B can slide along the Z axis [to simplify, between (0,0,0) and (0,0,2)]:
- Cx2 + Cy2 + Cz2 = 1
- Dx2 + Dy2 + Dz2 = 1
- Ex2 + Ey2 + Ez2 = 1
- Fx2 + Fy2 + Fz2 = 1
- Cx2 + Cy2 + (Cz - Bz)2 = 1
- Dx2 + Dy2 + (Dz - Bz)2 = 1
- Ex2 + Ey2 + (Ez - Bz)2 = 1
- Fx2 + Fy2 + (Fz - Bz)2 = 1
Authors of the construction of GeoGebra: Carlos Ueno and Rafael Losada