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Pregled bibliografske jedinice broj: 546355

Geometry of GS-quasigroups


Kolar-Begović, Zdenka; Kolar-Šuper, Ružica
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)


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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(abc)c=b, a(abc)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


Citiraj ovu publikaciju:

Kolar-Begović, Zdenka; Kolar-Šuper, Ružica
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)
Kolar-Begović, Z. & Kolar-Šuper, R. (2011) Geometry of GS-quasigroups. U: Terezia P. Vendel (ur.)MATEPOLLACK 2011, Mathematics in architecture and civil engineering design and education.
@article{article, author = {Kolar-Begovi\'{c}, Zdenka and Kolar-\v{S}uper, Ru\v{z}ica}, year = {2011}, pages = {20-20}, keywords = {GS-quasigroup, GS-trapezoids, affine-regular pentagon}, title = {Geometry of GS-quasigroups}, keyword = {GS-quasigroup, GS-trapezoids, affine-regular pentagon}, publisher = {Organising Comitee of "Mathematics in Architecture and Civil Engineering, Design and Education" conference}, publisherplace = {Pe\v{c}uh, Ma\djarska} }
@article{article, author = {Kolar-Begovi\'{c}, Zdenka and Kolar-\v{S}uper, Ru\v{z}ica}, year = {2011}, pages = {20-20}, keywords = {GS-quasigroup, GS-trapezoids, affine-regular pentagon}, title = {Geometry of GS-quasigroups}, keyword = {GS-quasigroup, GS-trapezoids, affine-regular pentagon}, publisher = {Organising Comitee of "Mathematics in Architecture and Civil Engineering, Design and Education" conference}, publisherplace = {Pe\v{c}uh, Ma\djarska} }




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