\((1+n)\) sequential dissection of a rectangle into \(m\)-gons, \(m\in \{ 3,5,6,7,8 \}\) (Q2821103)

For polygons \(P\) and \(Q\), a \textit{sequentially \((1+n)\)-\(P\)-\(Q\)-divisible dissection} is a partitioning of \(P\) into pairwise nonoverlapping subpolygons in such a way that for any \(j=1,2,\ldots, n\), the parts can be reassembled to a form one polygon similar to \(P\), and \(j\) polygons similar to \(Q\). Such a dissection is called \textit{trivial} if one of the subpolygons is similar to \(P\), and otherwise it is called \textit{nontrivial}.NEWLINENEWLINEThe authors present numerous, partly trivial and partly nontrivial sequentially \((1+n)\)-\(P\)-\(Q\)-divisible dissections for arbitrary values of \(n\), where \(P\) is a rectangle, and \(Q\) is an \(m\)-gon with \(m=3,5,6,7,\) or \(8\).