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.

The values of cos(pi/257) and cos(2pi/257) are 128-degree algebraic numbers.

Richelot and Schwendenwein found constructions for the 257-gon in 1832 (Coxeter 1969). DeTemple (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, Trigonometry Angles

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Weisstein, Eric W. "257-gon." From MathWorld--A Wolfram Web Resource.

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