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How to Find the Length of a Circle

How many sides does a polygon have to have before the perimeter is almost equal to a cirlce passing through each corner?
Notice how quickly the perimeter of the polygon and the cirlce become almost equal. π = 3.1415926535 8979323846 2643383279 5028841971....... see http://www.joyofpi.com/pi.html for more digits!!!