Naslov
Some geometric concepts in GS-quasigroups

Autori
Kolar-Begović, Zdenka ; Volenec, Vladimir

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Treći hrvatski matematički kongres : Zbornik / - Split : Hrvatsko matematičko društvo, 2004, 36-36

Skup
Hrvatski matematički kongres (3 ; 2004)

Mjesto i datum
Split, Hrvatska, 16.06.2004. - 18.06.2004

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
quasigroup

Sažetak
GS-quasigroup is an idempotent quasigroup which satisfies the (mutually equivalent) identities a(ab.c).c = b, a.(a.bc)c=b. The identities of mediality, elasticity, left and right distributivity and some other identities and equivalencies are also valid in a GS-quasigroup. The concept of GS-quasigroup is introduced by V.Volenec. Let C be the set of points in the Euclidean plane. If groupoid (C, .) is defined so that for any two different points a, b in C we define ab=c if the point b divides the pair a, c in the ratio of golden section, then (C, .) is a GS-quasigroup. That quasigroup will be denoted C((1+sqrt(5))/2) because we have c=(1+sqrt(5))/2 if a=0 and b=1.The figures in this quasigroup C((1+sqrt(5))/2) can be used for illustration of "geometrical" relations in any GS-quasigroup. In the general GS-quasigroup the concept of the parallelogram and midpoint can be introduced. The concept of the affine regular pentagon will be defined by means of GS-trapezoid. The concept of the affine regular dodecahedron and affine regular icosahedron is introduced by means of the affine regular pentagon. The concept of the affine regular decagon is introduced by means of the GS-deltoid. The geometrical representation of all introduced concepts will be given in the GS-quasigroup C((1+sqrt(5))/2) and the connection between them will be investigated.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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