The area of a regular 65537-gon is (with t = edge length) A whole regular 65537-gon is not visually discernible from a circle, and its perimeter differs from that of the circumscribed circle by about 15 parts per billion.

The regular 65537-gon (one with all sides equal and all angles equal) is of interest for being a constructible polygon: that is, it can be constructed using a compass and an unmarked straightedge.

The construction is very complex; Hermes spent 10 years completing the 200-page manuscript.

This method faces practical problems, as one of these Carlyle circles solves the quadratic equation x2 + x − 16384 = 0 (16384 being 214).

As 65,537 is prime, there are 32,767 regular forms generated by Schläfli symbols {65537/n} for all integers 2 ≤ n ≤ 32768 as