Chapter 12 - Vector-Valued Functions - 12.5 Curvature - Exercises Set 12.5 - Page 880: 43

$$\frac{2}{3}$$

We find: $\frac{\left|r^{2}+2\left(\frac{d r}{d \theta}\right)^{2}-r \frac{d^{2} r}{d \theta^{2}}\right|}{\left[r^{2}+\left(\frac{d r}{d \theta}\right)^{2}\right]^{3 / 2}}=\kappa$ $C A S:$ $\frac{8 \cos ^{2} 3 \theta+10}{\left(8 \cos ^{2} 3 \theta+1\right)^{3 / 2}}=\kappa(\theta)$ $\frac{2}{3}=\kappa(0)$