3320.21 – A Square Inside a Circle Inside a Square
Given a circle with radius , inscribe a square in it. Also circumscribe a square around it. What is the ratio of the perimeter of the outer square to the perimeter of the inner square?
Consult the figure. If we arrange that the two squares are in just the right relationship, then it is clear that if half of the outer edge is then the inner edge is . The ratio of the perimeters then is