Miklós Laczkovich

from Wikipedia, the free encyclopedia
Miklós Laczkovich (2011)

Miklós Laczkovich (born February 21, 1948 in Budapest ) is a Hungarian mathematician.

Life

Laczkovich studied at the Lorand Eötvös University in Budapest (graduated in 1971) and is a professor there. He is also a professor at University College London .

Laczkovich deals with real analysis and measure theory. In 1989 he solved Alfred Tarski's (1925) circle-squaring problem and thus showed that it is possible to divide a flat disk into a finite number of parts which can be combined to form a square with the same area. His proof was non-constructive as it made substantial use of the axiom of choice , and he also used a very large number (of the order of magnitude ) of parts. He also used non-measurable quantities for the parts. When assembling it in the proof it only got by with translations (without rotations). He also proved that such a decomposition is possible for any plane polygons and other surfaces bounded by sufficiently smooth curves. Thus Laczkovich's positive solution to the problem for such surfaces represents a partial analogue to the Banach-Tarski paradox in three or more dimensions.

In 1993 he received the Ostrowski Prize . He has been a corresponding member of the Hungarian Academy of Sciences since 1993 and a full member since 1998 . In 1998 he received the Széchenyi Prize . In 1992 he was invited speaker at the European Congress of Mathematicians in Paris (Paradoxical decompositions: a survey of recent results).

As a member of the A: N: S choir (tenor), with which he also recorded, he sings Renaissance choral music in his spare time.

Fonts

  • Conjecture and Proof , Mathematical Association of America, Washington DC 2001, ISBN 0-88385-722-7

Web links

Individual evidence

  1. Laczkovich Equidecomposability and discrepancy: a solution to Tarski's circle squaring problem , Journal für die Reine und Angewandte Mathematik, Vol. 404, 1990, pp. 77-117
  2. The dimension is not changed when the surfaces are broken down and reassembled. This is not possible in two dimensions because the Banach-Tarski paradox does not hold in two dimensions.
  3. Miklós Lazkovich's website at the Hungarian Academy of Sciences  ( page no longer available , search in web archivesInfo: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice.@1@ 2Template: Dead Link / mta.hu  
  4. ^ Website of the A: N: S choir