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

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home

EMIS Home

Pick a mirror

 		 

GEOMETRY OF PENTAGONAL QUASIGROUPS

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

Full text of the article: (for faster download, first choose a mirror)

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

© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
© 2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition