Some Ratios for Regular Inscribed Polygons
This Demonstration shows regular polygons, with three to 20 sides inscribed in a circle. The ratios of the radius to a side and the longest diagonal to a side are calculated. Two cases involve the golden ratio . For a pentagon, the ratio of a diagonal to a side is . For a 10-sided polygon, the ratio of the radius of the circle to a side of the decagon is .
 E. E. Kramer, The Mainstream of Mathematics, New York: Oxford University Press, 1951.