Gourt Home::Gourt :: Radius of curvature
In geometry, the radius of curvature of a curve at a point is the radius of the osculating circle at that point.
The more sharply curved, the smaller the radius of curvature.
Explanation in lay terms
Imagine driving a car on a curved road on a completely flat plain (so that the geographic plain is a geometric plane). At one point along the way, lock the steering wheel in its position, so that the car thereafter follows a perfect circle, possibly deviating from the road, which may be a more complicated curve than a circle. That circle is the osculating circle to the curve at the point at which the steering wheel was locked. The radius of that circle is the radius of curvature of the curved road at the point at which the steering wheel was locked.
Applications and examples
- For the use in differential geometry, see intrinsic coordinates.
See also
"Radius of curvature"