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). DeTemple (1991) gives a construction using 150 circles
(24 of which are Carlyle circles) which has geometrography symbol and simplicity
566.
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New York: Dover, p. 53, 1991.Klein, F. "The Construction of
the Regular Polygon of 17 Sides." Part I, Ch. 4 in "Famous Problems
of Elementary Geometry: The Duplication of the Cube, the Trisection of the Angle,
and the Quadrature of the Circle." In Famous
Problems and Other Monographs. New York: Chelsea, pp. 24-41, 1980.Pascal,
E. "Sulla costruzione del poligono regolare di 257 lati." Rendiconto
dell Accad. della scienze fisiche e matemat. sezione della Soc. a reale di Napoli,
Ser. 21, 33-39, 1887.Rademacher, H. Lectures
on Elementary Number Theory. New York: Blaisdell, 1964.Richelot,
F. J. "De resolutione algebraica aequationis , sive de divisione circuli per bisectionem anguli
septies repetitam in partes 257 inter se aequales commentatio coronata." J.
reine angew. Math.9, 1-26, 146-161, 209-230, and 337-358, 1832.Strommer,
J. "Konstruktion des regulären 257-Ecks mit Lineal und Streckenübertrager."
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