osculating plane

noun

, Mathematics.

1. the plane containing the circle of curvature of a point on a given curve.

Word History and Origins

Origin of osculating plane¹

First recorded in 1860–65

Example Sentences

Such a curve may be considered as described by a point, moving in a line which at the same time rotates about the point in a plane which at the same time rotates about the line; the point is a point, the line a tangent, and the plane an osculating plane, of the curve; moreover the line is a generating line, and the plane a tangent plane, of a developable surface or torse, having the curve for its edge of regression.

From Project Gutenberg

When a point of such a curve is given, the osculating plane is determined, hence all the curves through a given point with the same tangent have the same torsion.

From Project Gutenberg

That is to say, the osculating plane at any point of a geodetic line contains the normal to the surface at that point.

From Project Gutenberg

It cuts the osculating plane in a circle, called the circle of absolute curvature; and the centre and radius of this circle are the centre and radius of absolute curvature.

From Project Gutenberg

It cuts the osculating plane in a line called the principal normal.

From Project Gutenberg