7.53 Let $n$ be the maximum number of non-intersecting circles with a diameter of 1 whose centers are inside the polygon $M$, and let $m$ be the minimum number of circles with a radius of 1 required to cover the entire polygon $M$. Which is larger, $n$ or $m$?
[Solution] Suppose there are $n$ circles with diameters all equal to 1, which are mutually disjoint, and their centers $O_{1}, O_{2}, \cdots, O_{n}$ are all inside the polygon $M$. By taking $O_{1}, O_{2}, \cdots, O_{n}$ as centers, we draw circles with radius 1. Then these $n$ circles must cover the entire polygon $M$.

If not, there must be an inner point $A$ of $M$ that is not covered by these $n$ circles with radius 1. Thus, a circle with $A$ as the center and 1 as the diameter would not intersect with the original $n$ circles with diameter 1, which contradicts the maximality of $n$. This proves that $m \leqslant n$.

In the polygon shown in the right figure, we can take 3 points $O_{1}$, $O_{2}$, $O_{3}$ and draw 3 circles with them as centers and 1 as the diameter, which are mutually disjoint, so we know $n \geqslant 3$. However, the circumradii of $\triangle A B C$ and $\triangle A C D$ are both less than 1, thus $m \leqslant 2 < n$. For a square with diagonals less than 1, it is obvious that $m=n=1$ in this case. 

In summary, $m \leqslant n$ and both the equality and the inequality can be achieved.