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osculating circle
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The curvature at each point of a line is defined to be 1/r, where r is the radius of the osculating, or “kissing,” circle that best approximates the line at the given point.
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osculating circle

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The curvature at each point of a line is defined to be 1/r, where r is the radius of the osculating, or “kissing,” circle that best approximates the line at the given point.
The curvature at each point of a line is defined to be 1/r, where r is the radius of the osculating, or “kissing,” circle that best approximates the line at the given point.

The osculating circle is a concept in differential geometry that helps describe the curvature of a curve at a specific point. It is also known as the circle of curvature.

Essentially, the osculating circle is the circle that best approximates a curve at a given point. It shares the same tangent and curvature as the curve at that point. Its radius is equal to the radius of curvature of the curve. This concept was first defined by Gottfried Leibniz in 1686, who derived it from the Latin word osculare, meaning "to kiss".1

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3 Britannica Sources
  1. osculating circle
  2. differential geometry
  3. circle of curvature

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