39 On the plane, there are fixed points $A, B$. If for any $k$ points $P_{1}, P_{2}, \cdots, P_{k}$ on the plane, there exist two points $P_{i}, P_{j}(i, j \in\{1,2,3, \cdots, k\}, i \neq j)$ such that $\left|\sin \angle A P_{i} B-\sin \angle A P_{j} B\right|$ $\leqslant \frac{1}{1992}$, then the minimum value of $k$ is $\qquad$
391993 . From the problem, we know $\angle A P_{i} B \in[0, \pi], 0 \leqslant \sin \angle A P_{i} B \leqslant 1$. Dividing the interval $[0,1]$ into 1992 equal parts, the difference between any two values in each part must be $\leqslant \frac{1}{1992}$. To ensure that there are two sine values in one part, according to the pigeonhole principle, it is sufficient to have 1993 $P_{i}$, so the minimum value of $k$ is 1993.