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  • Autor
    • Lang, Johann
    • Mick, Sybille
    • Röschel, Otto
  • TitelRegularizing transformations of polygons
  • Datei
  • DOI10.1007/s00022-017-0373-3
  • Persistent Identifier
  • Erschienen inJournal of Geometry
  • Band108
  • Erscheinungsjahr2017
  • Heft2
  • Seiten791-801
  • ISSN1420-8997
  • ZugriffsrechteCC-BY
  • Download Statistik403
  • Peer ReviewNein
  • AbstractWe start with a generic n-gon \(Q_0\) with vertices \(q_{j,0}(j = 0, \ldots , n-1)\) in the d-dimensional Euclidean space \(\mathbb{E}^d\). Additionally, \(m+1\) real numbers \(u_0, \ldots, u_m \in \mathbb{R} (m < n) \) with \(\sum^m_{\mu=0} u_\mu = 1\) are given. From these initial data we iteratively define generations of n-gons \(Q_k\) in \(\mathbb{E}^d\) for \(k \in \mathbb{N}\) with vertices \( q_{j,k} := \sum^m_{\mu=0} u_\mu q_{j+\mu,k-1}\). We can show that this affine iteration generally regularizes in an affine sense.