Abstract:In 1796, Gauss succeeded in solving the problem of constructing the regular 17-gon with compass and straightedge. Later he proved that, using a compass and straightedge, it is possible to construct the regular polygons with $n=2^m n_1\cdots n_l$ sides if $n_1,\cdots, n_l$ are different prime numbers of the form $n_k=2^{2^{\nu_k}}+1$. Gauss also knew that only these regular polygons can be constructed but did not prove it.\linebreak P. Wantzel completed the result of Gauss and proved it in 1837. The present paper provides a new proof for Wantzel's theorem.
From: Johannes Mainik [view email]
[v1]
Thu, 25 Jun 2026 15:37:59 UTC (18 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。