Osculating Circle (Noun)
Meaning
The circle that touches a curve (on the concave side) and whose radius is the radius of curvature.
Classification
Nouns denoting attributes of people and objects.
Examples
- The osculating circle of a curve is the circle that most closely matches the curve at a given point.
- In differential geometry, the osculating circle is used to study the curvature of a curve and to make precise measurements.
- At each point on a curve, the osculating circle is the best possible approximation of the curve by a circle.
- A curve and its osculating circle have the same tangent line and the same curvature at the point of contact.
- The center of the osculating circle of a curve at a given point is the center of curvature and is located at a distance equal to the radius of curvature from the curve.