257 is a Fermat Prime, and the 257-gon is therefore a Constructible Polygon using Compass and Straightedge, as proved by Gauß. An illustration of the 257-gon is not included here, since its 257 segments so closely resemble a Circle. Richelot and Schwendenwein found constructions for the 257-gon in 1832 (Coxeter 1969). De Temple (1991) gives a construction using 150 Circles (24 of which are Carlyle Circles) which has Geometrography symbol and Simplicity 566.

**References**

Coxeter, H. S. M. *Introduction to Geometry, 2nd ed.* New York: Wiley, 1969.

De Temple, D. W. ``Carlyle Circles and the Lemoine Simplicity of Polygonal Constructions.'' *Amer. Math. Monthly*
**98**, 97-108, 1991.

Dixon, R. *Mathographics.* New York: Dover, p. 53, 1991.

Rademacher, H. *Lectures on Elementary Number Theory.* New York: Blaisdell, 1964.

© 1996-9

1999-05-25