two points on the spiral, A and B, with coordinates (3, -4) and (12, -8), respectively. I'd like to know the distance between these two points.
Recall that the equation of the Fermat spiral is given by $r = k\theta$, where $r$ is the radial distance from the origin, $\theta$ is the polar angle, and $k$ is a positive constant.
To find the distance between points A and B, we can use the distance formula:
$$\sqrt{(12 - 3)^2 + (-8 - (-4))^2} = \sqrt{9^2 + (-4)^2} = \sqrt{81 + 16} = \sqrt{97}$$
So, the distance between points A and B is $\boxed{\sqrt{97}}$.The answer is: \sqrt{97}