Geometry of GS-quasigroups (CROSBI ID 580196)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Kolar-Begović, Zdenka ; Kolar-Šuper, Ružica
engleski
Geometry of GS-quasigroups
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 $C(1/2(1+\sqrt 5))$.
GS-quasigroup; GS-trapezoids; affine-regular pentagon
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Podaci o prilogu
20-20.
2011.
objavljeno
Podaci o matičnoj publikaciji
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
Podaci o skupu
Mathematics in architecture and civil engineering design and education
pozvano predavanje
26.05.2011-28.05.2011
Pečuh, Mađarska