Perimeter of a Circle

Inscribe a circle within a square. Now break the sides of the square into successively smaller right angle segments that touch the circle. However you do this, the total length of these segments remains the same as the perimeter of the original square. The path containing the segments gradually approaches the circle. Hence the circle perimeter is shown to be that of the square! Well, maybe not. Try it below. Adjust the number of segment divisions. Breaking geometric objects into smaller pieces only tells us something if the metric of interest changes.