关于高斯对代数基本定理第三次证明的一种简化证明

A simplified proof of Gauss’s third proof of the Fundamental Theorem of Algebra

代数基本定理是代数学中一个非常重要且基础的定理,而冠以"数学王子"称号的德国数学家高斯(Johann Carl Friedrich Gauss,1777-1855)一生中为此定理提供了四次证明。本文依据原始文献及研究文献,着重分析相关数学家对高斯第三次证明的研究工作,在遵循高斯原始思想的前提下,针对第三次证明提出一种简化证明。

The fundamental theorem of algebra is a very important and basic theorem in algebra,and the German mathematician Johann Carl Friedrich Gauss (1777-1855),known as the "Prince of Mathematics",provided proof of this theorem four times in his life.Based on the original literature and research literature,this paper focuses on analyzing the research work of related mathematicians on the third proof of Gauss.On the premise of following the original idea of Gauss,a simplified proof is proposed for the third proof.