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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 $94S_1+47S_2+275C_1+0C_2+150C_3$ and Simplicity 566.

See also 65537-gon, Constructible Polygon, Fermat Prime, Heptadecagon, Pentagon


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 Eric W. Weisstein