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.

**References**

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

1999-05-25