Namespaces
Variants
Actions

Web of spheres

From Encyclopedia of Mathematics
Jump to: navigation, search

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.


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; System of subvarieties.

References

[a1] J.A. Todd, "Projective and analytical geometry" , Pitman (1947) pp. Chapt. VI
How to Cite This Entry:
Web of spheres. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Web_of_spheres&oldid=31690
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article