EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 99(113), pp. 109–120 (2016)

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Stipe Vidak

Department of Mathematics, University of Zagreb, Zagreb, Croatia

Abstract: Pentagonal quasigroups are IM-quasigroups in which the additional identity of pentagonality holds. Motivated by the example $C(q)$, where $q$ is a solution of the equation $q^4-3q^3+4q^2-2q+1=0$, some basic geometric concepts are introduced and studied in a general pentagonal quasigroup. Such concepts are parallelogram, midpoint of a segment, regular pentagon and regular decagon. Some theorems of Euclidean plane which use these concepts are stated and proved in pentagonal quasigroups.

Keywords: IM-quasigroup; parallelogram; midpoint; regular pentagon; regular decagon

Classification (MSC2000): 20N05

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Electronic fulltext finalized on: 12 Apr 2016. This page was last modified: 20 Apr 2016.

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