Napoleon’s quasigroups

Mathematica Slovaca

Vedran Krčadinac¹ 

关键词: medial quasigroup;    Napoleon’s theorem;   

DOI  :  10.2478/s12175-011-0055-9

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

Napoleon’s quasigroups are idempotent medial quasigroups satisfying the identity (ab·b)(b·ba) = b. In works by V. Volenec geometric terminology has been introduced in medial quasigroups, enabling proofs of many theorems of plane geometry to be carried out by formal calculations in a quasigroup. This class of quasigroups is particularly suited for proving Napoleon’s theorem and other similar theorems about equilateral triangles and centroids.

【 授权许可】

Unknown