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# Regular Nonagon

The regular nonagon is the regular polygon with nine sides and Schläfli symbol .

The regular nonagon cannot be constructed using the classical Greek rules of geometric construction, but Conway and Guy (1996) give a Neusis construction based on angle trisection. Madachy (1979) illustrates how to construct a nonagon by folding and knotting a strip of paper. Although the regular nonagon is not a constructible polygon, Dixon (1991) gives constructions for several angles which are close approximations to the nonagonal angle , including angles of and .

Given a regular nonagon, let be the midpoint of one side, be the mid-arc point of the arc connecting an adjacent side, and the midpoint of . Then, amazingly, (Karst, quoted in Bankoff and Garfunkel 1973).

Nonagram, Polygon, Regular Polygon, Trigonometry Angles--Pi/9

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## References

Bankoff, L. and Garfunkel, J. "The Heptagonal Triangle." Math. Mag. 46, 7-19, 1973.Bold, B. Famous Problems of Geometry and How to Solve Them. New York: Dover, pp. 60-61, 1982.Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 194-200, 1996.Dixon, R. Mathographics. New York: Dover, pp. 40-44, 1991.Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 60-61, 1979.

## Cite this as:

Weisstein, Eric W. "Regular Nonagon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RegularNonagon.html