Definition:Curvature/Whewell Form

Definition

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

The curvature $\kappa$ of $C$ at a point $P$ can be expressed in the form of a Whewell equation as:

$\kappa = \dfrac {\d \psi} {\d s}$

where:

$\psi$ is the turning angle of $C$

$s$ is the arc length of $C$.

Also see

• Equivalence of Definitions of Curvature

• Results about curvature can be found here.

Sources

• 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