Chapter 12 - Vector-Valued Functions - 12.5 Curvature - Exercises Set 12.5 - Page 879: 22

False

This statement is false because the radius of the osculating circle to a curve $\mathcal{C}$ at a point $\mathbf{P}$ is given by the expression: \[ \rho = \frac{1}{\kappa} \] which means the radius is equal to the reciprocal value of the curvature at point $\mathbf{P}$. Result: False