Constructing the $\mathbf{2^{2^5} + 1 = F_5}$-gon: the first step, the 641-gon

Helmut Ruhland

Constructing the $\mathbf{2^{2^5} + 1 = F_5}$-gon: the first step, the 641-gon

Number Theory 2026-07-04 v1

Authors: Helmut Ruhland

Abstract

In an article S. Adlaj showed the construction of the $F_4 = 65\,537$ -gon ( $F_4$ a Fermat prime). Extending the authors method to cases, where the multiplicative group is not of order $2^n$ , but has an additional prime factor, here the $641$ -gon ist constructed. $641$ is the smaller prime factor of the composite Fermat number $F_5 = 2^{2^5} + 1$ .

Keywords

constructible polygons Fermat numbers Fermat primes 641-gon geometric construction

Cite

@article{arxiv.2607.04000,
  title  = {Constructing the $\mathbf{2^{2^5} + 1 = F_5}$-gon: the first step, the 641-gon},
  author = {Helmut Ruhland},
  journal= {arXiv preprint arXiv:2607.04000},
  year   = {2026}
}

Comments

7 pages