center of curvature
Definition
Noun: - The center of the circle of curvature: In geometry, the center of curvature is the fixed point that is the center of the osculating circle at a given point on a curve. This circle best approximates the curve at that point.
Usage
The term "center of curvature" is used in mathematics, physics, and engineering to describe a specific geometric property of a curve at a point. - To find the radius of curvature, you must first locate the center of curvature. - The path of the light ray depends on the center of curvature of the lens surface.
Advanced Usage
- In differential geometry: The center of curvature is a point on the evolute of the curve. The locus of all centers of curvature for a curve forms its evolute.
- The evolute is defined as the set of all centers of curvature of the original curve.
Variants and Related Words
- Centre of curvature: The British English spelling variant.
- Curvature center: A less common alternative phrasing.
- Circle of curvature (noun): The osculating circle itself, for which the center of curvature is the center.
- Radius of curvature (noun): The distance from a point on the curve to its center of curvature.
Synonyms
- None direct: This is a precise technical term. In context, one might refer to the "focal point" for certain optical applications, but this is not a true synonym.
Related Phrases
- Instantaneous center of rotation: In kinematics, a related but distinct concept for the motion of a rigid body.
Related Idioms
- N/A: This is a scientific term and is not used idiomatically.
Noun
-
the center of the circle of curvature
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