Naslov
Affine regular decagons in GS--quasigroup

Autori
Kolar-Begović, Zdenka ; Kolar-Šuper, Ružica ; Volenec, Vladimir

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

Izvornik
Abstracts, Loops'07 / - Prag, 2007, 16-16

Skup
Loops'07

Mjesto i datum
Prag, Češka Republika, 19.08.2007. - 25.08.2007

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
GS-quasigroup ; affine-regular decagon

Sažetak
A GS--qusigroup is defined as an idempotent quasigroup which satisfies the mutually equivalent identities $a(ab \cdot c)\cdot c=b$, $a \cdot (a \cdot bc)c=b$. Some interesting geometric concepts can be defined in a general GS--quasigroup. The concept of the affine regular decagon and affine regular star shaped decagon in a general GS--quasigroup will be defined through the concept of GS--deltoid. Introducing a number of new points besides the vertices of affine regular decagon some statements about parallelograms and affine regular pentagons will be proved. Using obtained points it will be shown how to construct the affine regular icosahedron from the affine regular decagon. The geometrical representation of the introduced concepts and relations between them will be given in the GS--quasigroup $C(1\2(1+\sqrt 5 ))$

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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