Web of spheres
The collection of all spheres for which a given point (the centre of the web, or the radical centre) has a given power $p$ (the power of the web). There are three types of webs of spheres:
1) a hyperbolic web $(p>0)$, consisting of all spheres orthogonal to a given sphere;
2) an elliptic web $(p<0)$, consisting of all spheres intersecting a given sphere in a great circle of the latter;
3) a parabolic web $(p=0)$, consisting of all spheres passing though a given point.
The collection of all spheres common to two webs is called a net of spheres. The collection of all common spheres to three webs with centres not on a straight line is called a pencil of spheres.
|[a1]||J.A. Todd, "Projective and analytical geometry" , Pitman (1947) pp. Chapt. VI|
Web of spheres. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Web_of_spheres&oldid=31690