Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 48, No. 2, pp. 423434 (2007) 

Squaring the circle via affine congruence by dissection with smooth piecesChristian RichterMathematisches Institut, FriedrichSchillerUniversität, D07737 Jena, Germany, email:richterc@minet.unijena.deAbstract: For every $k \ge 2$, we construct a dissection of a square into finitely many topological discs, each having a piecewise $k$ times differentiable boundary, such that images of these pieces under appropriate maps of the group $\bf{A}ff_+$ of orientation preserving affine transformations of the plane form a dissection of a circular disc. The dissections consist of six pieces in the case $k=2$ and of $14$ pieces for every $k \ge 3$. Keywords: squaring the circle, congruence by dissection, topological disc with piecewise smooth boundary, affine transformation Classification (MSC2000): 52B45 Full text of the article:
Electronic version published on: 7 Sep 2007. This page was last modified: 28 Jun 2010.
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