Chapter 12 - Vector-Valued Functions - 12.5 Curvature - Exercises Set 12.5 - Page 880: 42

$$\frac{1}{\sqrt{5} e^{2}}$$

We find: $\frac{\left|r^{2}+2\left(\frac{d r}{d \theta}\right)^{2}-r \frac{d^{2} r}{d \theta^{2}}\right|}{\left[r^{2}+\left(\frac{d r}{d \theta}\right)^{2}\right]^{3 / 2}}=\kappa$ $C A S:$ $\frac{1}{\sqrt{5} e^{2 \theta}}=\kappa(\theta)$ $\frac{1}{\sqrt{5} e^{2}}=\kappa(1)$