Some Ratios for Regular Inscribed Polygons

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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 .

Contributed by: Walter Zhao (June 2016)
Open content licensed under CC BY-NC-SA




[1] E. E. Kramer, The Mainstream of Mathematics, New York: Oxford University Press, 1951.

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