View source for 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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/w/w097/w097300/w0973001.png" /> (the power of the web). There are three types of webs of spheres:

1) a hyperbolic web <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/w/w097/w097300/w0973002.png" />, consisting of all spheres orthogonal to a given sphere;

2) an elliptic web <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/w/w097/w097300/w0973003.png" />, consisting of all spheres intersecting a given sphere in a great circle of the latter;

3) a parabolic web <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/w/w097/w097300/w0973004.png" />, consisting of all spheres passing though a given point.

The collection of all spheres common to two webs is called a [[Net|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.



====Comments====
Instead of  "web of spheres"  one also finds the terminology  "bundle of spheres"  and  "net of spheres" . Cf. (the editorial remarks to) [[Linear system|Linear system]]; [[System of subvarieties|System of subvarieties]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.A. Todd,   "Projective and analytical geometry" , Pitman  (1947)  pp. Chapt. VI</TD></TR></table>