Naslov
The Napoleon-Barlotti theorem in hexagonal quasigroups

Autori
Vidak, Stipe ; Bombardelli, Mea

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
6th Croatian Mathematical Congress

Mjesto i datum
Zagreb, Hrvatska, 14.06.2016. - 17.06.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
IM-quasigroup, hexagonal quasigroup, regular triangle, regular hexagon

Sažetak
Hexagonal quasigroups are idempotent medial quasigroups in which the additional identity of semisymmetricity, a b ⋅ a = b ab⋅a=b, holds. The famous Napoleon-Barlotti theorem of Euclidean geometry says: The centres of the regular n n- gons constructed on the sides of an affine regular n n-gon form a regular n n-gon. In this talk the concepts of parallelogram, regular triangle and its centre, regular hexagon and its centre and affine regular hexagon are introduced in hexagonal quasigroups. Some illustrations of these concepts are given in the model C ( q ) C(q), where q q is a solution of the equation q 2 − q + 1 = 0 q2−q+1=0. The Napoleon-Barlotti theorem in the cases n = 3 n=3 and n = 6 n=6 is stated and proved in a general hexagonal quasigroup.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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