Napoleon's quasigroups

Year, pages: 2011, 885 - 894

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.

Krčadinac, V. 2011. Napoleon's quasigroups. In Mathematica Slovaca, vol. 61, no.6, pp. 885-894. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0055-9

Krčadinac, V. (2011). Napoleon's quasigroups. Mathematica Slovaca, 61(6), 885-894. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0055-9