Stanisław Świerczkowski
| Stanisław Świerczkowski | |
|---|---|
| Born |
July 16, 1932 Toruń, Poland |
| Died | September 30, 2015 (aged 83) Australia |
| Residence | Australia |
| Nationality | Polish |
| Alma mater | University of Wroclaw, |
| Known for | Three-Distance Theorem, Non-Tetratorus Theorem |
| Children | 2 |
| Awards | Foundation of Alfred Jurzykowski (1996) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Glasgow University, University of Sussex, University of Washington, Australian National University, Sultan Qaboos University, Queen’s University, University of Colorado at Boulder |
| Doctoral advisor | Hugo Steinhaus |
Stanisław (Stash) Świerczkowski (July 16, 1932 – September 30, 2015) was a Polish mathematician famous for his solutions to two iconic problems posed by Hugo Steinhaus: the Three-Distance (or Three-Gaps) Theorem and the Non-Tetratorus Theorem.
Stanisław (Stash) Świerczkowski was born in Toruń, Poland. His parents were divorced during his infancy. When war broke out his father was captured in Soviet-controlled Poland and murdered in the 1940 Katyń Massacre. He belonged to the Polish nobility; Świerczkowski's mother belonged to the upper middle class and would have probably suffered deportation and murder by the Nazis. However she had German connections and was able to gain relatively privileged class 2 Volksliste citizenship. At the end of the war Świerczkowski's mother was forced into hiding near Toruń until she was confident that she could win exoneration from the Soviet-controlled government for her Volksliste status and be rehabilitated as a Polish citizen. Meanwhile, Świerczkowski lived in a rented room in Toruń and attended school there.
Świerczkowski won a university place to study astronomy at the University of Wrocław but switched to mathematics to avoid the drudgery of astronomical calculations. He discovered a natural ability through his friendship with Jan Mycielski and was able to remain at Wrocław to complete his masters under Jan Mikusiński. He graduated with a PhD in 1960, his dissertation including the now-famous Three-Distance Theorem which he proved in 1956 in answer to a question of Hugo Steinhaus.
The Three-Distance (or Three-Gaps) Theorem says: take arbitrarily many integer multiples of an irrational number between zero and one and plot them as points around a circle of unit circumference; then at most three different distances will occur between consecutive points. This answered a question of Hugo Steinhaus. The theorem belongs to the field of Diophantine approximation since the smallest of the three distances observed may be used to give a rational approximation to the chosen irrational number. It has been extended and generalized in many ways.
The Non-Tetratorus Theorem, published by Świerczkowski in 1958 says that it is impossible to construct a closed chain (torus) of regular tetrahedra, placed face to face. Again this answered a question of Hugo Steinhaus. The result is attractive and counter-intuitive since the tetrahedron is unique among the Platonic solids in having this property. Recent work by Michael Elgersma and Stan Wagon has sparked new interest in this result by showing that, experimentally, one can create chains of tetrahedra which are arbitrarily close to be being closed. Theoretical confirmation of this property is an open problem, it is known to be true if chains are allowed to self-intersect.
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