On the Set-Theoretical Circle-Squaring Problem

by    Eike Hertel

Preprint series: 00-06, Reports on Algebra and Geometry

The paper is published: Jenaer Schriften zur Mathematik und Informatik, Math/Inf/00/04, Universität Jena, Germany, 2000

52B45 Dissections and valuations (Hilbert's third problem, etc.)

Abstract: The set-theoretical circle-squaring problem goes back to
A. Tarski: Can a circle be partitioned into sets that can
be reassembled to form a square? We give a short survey on
results to this question and prove the impossibility of the
circle-squaring with respect to similarities and using
elementary sets as pieces of the dissection.

Keywords: Equidissectability Similarities

Upload: 2000-03-31

Update: 2000-04-03

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