A student says that in a square-root spiral, each new radius is obtained by directly adding 1 to the previous radius. What is the correct evaluation of this statement?

Correct answer: The statement is incorrect; the square of the new radius is 1 more than the square of the previous radius.

At each step, the new unit side is perpendicular to the previous radius. Thus Pythagoras gives \(r_{\text{new}}^2=r_{\text{old}}^2+1\), not \(r_{\text{old}}+1\). Exam tip: compare squares of successive radii.