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.

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.

单词	osculating sphere
释义	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. 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.
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