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Geometry of pentagonal quasigroups
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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 q4?3q3+4q2?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.
Title: Geometry of pentagonal quasigroups
Description:
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 q4?3q3+4q2?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.
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