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

GEOMETRY OF PENTAGONAL QUASIGROUPSStipe VidakDepartment of Mathematics, University of Zagreb, Zagreb, CroatiaAbstract: Pentagonal quasigroups are IMquasigroups in which the additional identity of pentagonality holds. Motivated by the example $C(q)$, where $q$ is a solution of the equation $q^43q^3+4q^22q+1=0$, 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: IMquasigroup; 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
