engleski

Affine regular decagons in GS--quasigroup

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 $C(1\2(1+\sqrt 5 ))$

GS-quasigroup ; affine-regular decagon

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