Osculating circle of a curve

Definitions

• Webster's Revised Unabridged Dictionary
• Osculating circle of a curve (Geom) the circle which touches the curve at some point in the curve, and close to the point more nearly coincides with the curve than any other circle. This circle is used as a measure of the curvature of the curve at the point, and hence is called circle of curvature.
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Usage

In science:

Proof: A circle that lies in the dual osculating plane of the point eα (s) on the dual timelike curve eα and that has the centre M = eα (s) + 1 κ N lying on the dual principal normal N of the point eα (s) and the radius 1 κ far from eα (s), is called dual osculating circle of the dual curve eα in the point eα (s).
On dual timelike - spacelike Mannheim partner curves in ID3 1
Proof: A circle that lies in the dual osculating plane of the point eα (s) on the dual timelike curve eα and that has the centre M = eα (s) + 1 κ N lying on the dual principal normal N of the point eα (s) and the radius 1 κ far from eα (s), is called dual osculating circle of the dual curve eα in the point eα (s).
On Dual Timelike Mannheim Partner Curves in D3 1
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