Curvature

Definition

Curvature refers to how much a curve deviates from being a straight line at any given point. It measures the rate at which the direction of a curve is changing.

Analogy

Imagine driving on a winding road. The curvature of the road determines how sharp or gradual the turns are. A high curvature means you have to make frequent and sharp turns, while a low curvature means the road is mostly straight with gentle curves.

Related terms

Tangent Line: A tangent line is a straight line that touches a curve at only one point, without crossing it. It represents the instantaneous direction of the curve at that point.

Radius of Curvature: The radius of curvature is the radius of the circle that best approximates a curve at any given point. It indicates how tightly or loosely the curve bends.

Osculating Circle: An osculating circle is a circle that has exactly one point in common with a given curve and shares both its tangent line and curvature with that point on the curve.