Chapter 11, Problem 15P

Suppose that circles of equal diameter are packed tightly in n rows inside an equilateral triangle. (The figure illustrates the case n = 4.) If A is the area of the triangle and A_n is the total area occupied by the n rows of circles, show that

$\underset{n\to \infty }{\lim }\frac{A_n}{A}=\frac{\pi }{2\sqrt{3}}$

FIGURE FOR PROBLEM 15