Definition:Center of Curvature

Definition

Let $C$ be a curve embedded in the plane.

Let $N$ be the normal to $C$ at a point $P$.

Let $\rho$ be the radius of curvature of $C$ at $P$.

Let $Q$ be the point on $N$ which is at a distance $\rho$ from $P$ on the concave side of $C$.

$Q$ is known as the center of curvature of $C$ at $P$.

Linguistic Note

The British English spelling of center is centre.

The convention on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to use the American English spelling center, but it is appreciated that there may be lapses.

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): centre of curvature
• 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): centre of curvature
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): curvature