Zur Affingeometrie konvexer Polygone

by    E. Hertel

Preprint series: 00-09, Reports on Algebra and Geometry

The paper is published: Jenaer Schriften zur Mathematik und Informatik, Math/Inf/00/22, Universität Jena, 2000

52B45 Dissections and valuations (Hilbert's third problem, etc.)
51N10 Affine analytic geometry

Abstract: A convex $n$-gon $\CP$ is called $k$-self-affine if $\CP$
can be dissected into $k \ge 2$ $n$-gons, each affine
equivalent to $\CP$.
Each triangle is trivially $k$-self-affine for all
$k \ge 2$. It is proved that for self-affine convex
$n$-gons holds $n \le 5$ and conjectured $n < 5$. For the
(only interesting) quadrangles first results for $k=2,3$
are given.

Keywords: polygons, selfaffinity

Upload: 2000-08-18

Update: 2000-08-21

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