An infinite class of movable 5-configurations (Q2827793)

\textit{B. Grünbaum} wrote in his book [Configurations of points and lines. Providence, RI: American Mathematical Society (AMS) (2009; Zbl 1205.51003), p. 23]: ``There has been no investigation of \(5\)-configurations \dots till very recently, and no systematic approaches have been developed so far.'' The present paper helps to fill this gap, since it presents a new construction that produces infinitely many geometric \(5\)-configurations which are movable.NEWLINENEWLINEThe new construction uses the crossing spans lemma [\textit{L. W. Berman}, Electron. J. Comb. 13, No. 1, Research paper R104, 30 p. (2006; Zbl 1109.51003)] and the circumcircle construction lemma [\textit{L. W. Berman} and \textit{J. R. Faudree}, Discrete Comput. Geom. 49, No. 3, 671--694 (2013; Zbl 1270.51008)]. The building blocks of the new construction of \(5\)-configurations are celestial \(4\)-configurations for which the authors present a construction algorithm. In a second algorithm which starts from a celestial \(4\)-configuration, the authors construct a \(5\)-configuration. Moreover, they prove:NEWLINENEWLINE1. There exist infinitely many \(5\)-configurations with one continuous degree of freedom.NEWLINENEWLINE2. There exists at least one \(5\)-configuration with \(s\) continuous degrees of freedom, for infinitely many values of \(s\).NEWLINENEWLINEFinally, three open problems are posed.