From a piece of wire to pi.

Take a fixed length and break it into equal segments to form a regular polygon. This polygon has a circumscribed circle. The radii segments from the center of that circle to the vertices of the polygon are all congruent, and can be calculated. Divide the fixed length, in this case 3, by the diameter (double the calculated radius) gets an approximation for pi. Increase the number of equal segments, and repeat.