Osculating Sphere

osculating sphere

[¦äs·kyə‚lād·iŋ ′sfir]
(mathematics)
For a curve C at a point p, the limiting sphere obtained by taking the sphere that passes through p and three other points on C and then letting these three points approach p independently along C.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Osculating Sphere

 

The osculating sphere of a space curve l at a point M is the sphere having contact of order n ≥ 3 with l at M. The osculating sphere can also be defined as the limit of a variable sphere passing through four points of l as the points tend to M.

The radius of the osculating sphere is

where ρ is the radius of curvature of l at M, ̓ is the torsion of l, and ds is the differential of arc of l.

REFERENCE

Rashevskii, P. K. Kurs differentsial’noi geomelrii, 4th ed. Moscow, 1956.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
If its pseudo-Galilean trihedron is {t(x), n(x), b(x)}, then the center of osculating sphere of r at the point r(x) is given by
If its pseudo-Galilean trihedron {t(x), n(x), b(x)}; then the center of osculating sphere of r at the point r(x) is given by