Pregled bibliografske jedinice broj: 546355
Geometry of GS-quasigroups
Geometry of GS-quasigroups // MATEPOLLACK 2011, Mathematics in architecture and civil engineering design and education / Terezia P. Vendel (ur.).
Komló: Organising Comitee of "Mathematics in Architecture and Civil Engineering, Design and Education" conference, 2011. str. 20-20 (pozvano predavanje, međunarodna recenzija, sažetak, znanstveni)
CROSBI ID: 546355 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
Geometry of GS-quasigroups
Autori
Kolar-Begović, Zdenka ; Kolar-Šuper, Ružica
Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni
Izvornik
MATEPOLLACK 2011, Mathematics in architecture and civil engineering design and education
/ Terezia P. Vendel - Komló : Organising Comitee of "Mathematics in Architecture and Civil Engineering, Design and Education" conference, 2011, 20-20
Skup
Mathematics in architecture and civil engineering design and education
Mjesto i datum
Pečuh, Mađarska, 26.05.2011. - 28.05.2011
Vrsta sudjelovanja
Pozvano predavanje
Vrsta recenzije
Međunarodna recenzija
Ključne riječi
GS-quasigroup; GS-trapezoids; affine-regular pentagon
Sažetak
A golden section quasigroup (shortly GS-quasigroup) is defined as an idempotent quasigroup which satisfies the mutually equivalent identities a(abc)c=b, a(abc)c=b. In this presentation identities and relations which are valid in a general GS-quasigroup will be researched. The geometrical meaning of the obtained identites will be given in the GS-quasigroup $C(1/2(1+\sqrt 5))$. Some interesting geometric concepts can be defined in a general GS-quasigroup. Namely, in a general GS-quasigroup the geometrical concept of the parallelogram, GS-trapezoid and some other geometric concepts can be introduced. The geometric concept of an affine-regular pentagon can be defined by means of GS-trapezoids. The concept of an affine-regular dodecahedron and affine-regular icosahedron can be obtained using the affine regular pentagons. Algebraic proofs of the statements about properties of the geometric concepts and the relationships between them in a general GS-quasigroup will be presented by means of the identities which are valid in a general GS-quasigroup. The geometrical representation of the introduced concepts and the obtained relations between them will be given in the GS-quasigroup $C(1/2(1+\sqrt 5))$.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
037-0372785-2759 - Neasocijativne algebarske strukture i njihove primjene (Volenec, Vladimir, MZOS ) ( CroRIS)
Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Sveučilište u Osijeku, Odjel za matematiku,
Fakultet za odgojne i obrazovne znanosti, Osijek