Pi as an arc length

One way of computing pi is to compute the arc length of the first quadrant of the unit circle, then multiply by 2. One way of computing the length of any curve is to approximate it by a broken-line path, as in the figure eventually to be placed below. The length of the broken-line figure will approximate the length of the curve. If there are very many short line segments the approximation will be a good one.

To find the length of the broken-line path we find the length of each of its segments, then add them up.

Using this idea, write a program to compute an approximate value of pi.