TOPICS
257-gon
257 is aFermat prime, and the 257-gon is therefore aconstructible polygon usingcompass andstraightedge, as proved by Gauss. An illustration of the 257-gon is not included here, since its 257 segments so closely resemble acircle.
The values of
and
are 128-degreealgebraic numbers.
Richelot and Schwendenwein found constructions for the 257-gon in 1832 (Coxeter 1969). DeTemple (1991) gives a construction using 150circles (24 of which areCarlyle circles) which hasgeometrography symbol
andsimplicity 566.
See also
65537-gon,Constructible Polygon,Fermat Prime,Heptadecagon,Pentagon,Trigonometry AnglesExplore with Wolfram|Alpha
References
Bachmann, P.Die Lehre von der Kreistheilung und ihre Beziehungen zur Zahlentheorie. Leipzig, Germany: Teubner, 1872.Bold, B.Famous Problems of Geometry and How to Solve Them. New York: Dover, p. 70, 1982.Coxeter, H. S. M.Introduction to Geometry, 2nd ed. New York: Wiley, 1969.DeTemple, D. W. "Carlyle Circles and the Lemoine Simplicity of Polygonal Constructions."Amer. Math. Monthly98, 97-108, 1991.Dickson, L. E. "Constructions with Ruler and Compasses; Regular Polygons." Ch. 8 inMonographs on Topics of Modern Mathematics Relevant to the Elementary Field (Ed. J. W. A. Young). New York: Dover, pp. 352-386, 1955.Dixon, R.Mathographics. 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." InFamous 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."Acta Math. Hungar.70, 259-292, 1996.Trott, M. "
à la Gauss."Mathematica Educ. Res.4, 31-36, 1995.Referenced on Wolfram|Alpha
257-gonCite this as:
Weisstein, Eric W. "257-gon." FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/257-gon.html