Definition:Curvature/Reciprocal of Radius of Osculating Circle

Definition

Let $C$ be a curve defined by a real function which is twice differentiable.

The curvature of $C$ is defined as:

the reciprocal of the radius of the osculating circle to $C$.

Also see

• Equivalence of Definitions of Curvature

• Results about curvature can be found here.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.23$: Evolutes and Involutes. The Evolute of a Cycloid
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): curvature
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): curvature

• Weisstein, Eric W. "Curvature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Curvature.html