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Glite Dictionary
circle of curvature

circle of curvature

9.9
A circle that touches a curve on its inside and matches its bend there
  • noun
  • Specialized
translation icon : círculo de curvatura
  • At any point on a smooth curve, you can construct a circle of curvature that best approximates the local geometry.

Examples

  • The radius of the circle of curvature at a specific point indicates how tightly the curve is bending.

  • The radius of the circle of curvature changes along the shape of the curve.

  • In differential geometry, the circle of curvature plays a key role in analyzing curves.

  • The circle of curvature is essential in differential geometry.

  • Can you explain the circle of curvature at this point?

  • At any point on a smooth curve, you can construct a circle of curvature that best approximates the local geometry.

  • In differential geometry, the circle of curvature is crucial for understanding the bending of curves.

Synonyms

osculating circle
vscircle of curvature
  • Specialized
9.9

A circle that touches a curve at one point and matches its bend near that spot

is an alternative name used for the same geometric circle and radius

Surface Forms

circle of curvature singular
circles of curvature plural

Morphology

circle + of + curvature

The compound clearly links 'circle' with 'curvature', so a learner who knows both words can infer it denotes a circle related to the curvature of a curve. However, the precise technical sense (the osculating circle that touches the curve at a point with radius equal to the radius of curvature on the concave side) is domain-specific and not fully predictable from everyday meanings, so full understanding requires mathematical knowledge.

Etymology

The noun circle of curvature is like a small circle that 'hugs' a curve at one point on the inside where the line bends. The circle's size shows how much the curve bends there, so the circle of curvature is an easy way to 'measure' or match the curve at that point.