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65537 is the largest known Fermat Prime, and the 65537-gon is therefore a Constructible Polygon using Compass and Straightedge, as proved by Gauß. The 65537-gon has so many sides that it is, for all intents and purposes, indistinguishable from a Circle using any reasonable printing or display methods. Hermes spent 10 years on the construction of the 65537-gon at Göttingen around 1900 (Coxeter 1969). De Temple (1991) notes that a Geometric Construction can be done using 1332 or fewer Carlyle Circles.

See also 257-gon, Constructible Polygon, 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.

© 1996-9 Eric W. Weisstein