Three, (16 points) Divide each side of an equilateral triangle with side length $a$ into 1993 equal parts, then connect the corresponding points on each side with parallel lines, resulting in several smaller equilateral triangles. Find the sum of the areas of the incircles of all the smaller equilateral triangles.


$$
\begin{array}{l} 
\text { Three, the number of small equilateral triangles is } \\
1+3+5+\cdots+(2 \times 1993 \\
-1)=1993^{2} .
\end{array}
$$

The height of each small equilateral triangle is
$$
\frac{\sqrt{3}}{2} a \cdot \frac{1}{1993} \text {, }
$$

The radius of the incircle of each small equilateral triangle is
$$
\frac{\sqrt{3}}{2} a \cdot \frac{1}{1993} \cdot \frac{1}{3} \text {, }
$$
$\therefore$ The area of the incircle of each small equilateral triangle is
$$
\pi\left(\frac{\sqrt{3}}{2} a \cdot \frac{1}{1993} \cdot \frac{1}{3}\right)^{2} \text {. }
$$

Therefore, the sum of the areas of the incircles of all $1993^{2}$ small equilateral triangles is
$$
S=1993^{2} \cdot \pi\left(\frac{\sqrt{3}}{2} a \cdot \frac{1}{1993} \cdot \frac{1}{3}\right)^{2}=\frac{\pi a^{2}}{12} .
$$