László Fejes Tóth

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The native form of this personal name is Fejes Tóth László. This article uses Western name order when mentioning individuals.
László Fejes Tóth
László Fejes Tóth, 1991
Born
László Tóth

(1915-03-12)12 March 1915
Szeged, Hungary
Died17 March 2005(2005-03-17) (aged 90)
Budapest, Hungary
AwardsKossuth Prize (1957), State Award (1973), Gauss Bicentennial Medal (1977), and Gold Medal of the Hungarian Academy of Sciences (2002)
Academic background
Alma materPázmány Péter University, as of 1950 Eötvös Loránd University
Academic work
Main interestsDiscrete and combinatorial geometry
Notable worksLagerungen in der Ebene, auf der Kugel und im Raum; Regular Figures
Notable ideasTheorems on packings and coverings of geometrical objects, including the packing of spheres
InfluencedThomas Hales, Károly Bezdek

László Fejes Tóth (Hungarian: Fejes Tóth László, pronounced [ˈfɛjɛʃ ˈtoːt ˈlaːsloː] 12 March 1915 – 17 March 2005) was a Hungarian mathematician who specialized in geometry. He proved that a lattice pattern is the most efficient way to pack centrally symmetric convex sets on the Euclidean plane (a generalization of Thue's theorem, a 2-dimensional analog of the Kepler conjecture).[1] He also investigated the sphere packing problem. He was the first to show, in 1953, that proof of the Kepler conjecture can be reduced to a finite case analysis and, later, that the problem might be solved using a computer.

He was a member of the Hungarian Academy of Sciences (from 1962) and a director of the Alfréd Rényi Institute of Mathematics (1970-1983). He received both the Kossuth Prize (1957) and State Award (1973).[2][3]

Together with H.S.M. Coxeter and Paul Erdős, he laid the foundations of discrete geometry.[4][5][6]

Early life and career

As described in a 1999 interview with István Hargittai, Fejes Tóth's father was a railway worker, who advanced in his career within the railway organization ultimately to earn a doctorate in law. Fejes Tóth's mother taught Hungarian and German literature in a high school. The family moved to Budapest, when Fejes Tóth was five; there he attended elementary school and high school—the Széchenyi István Reálgimnázium—where his interest in mathematics began.[3]

Fejes Tóth attended

proceedings of the French Academy of Sciences—1935.[3][7] He then received his doctorate at Pázmány Péter University, under the direction of Lipót Fejér.[8]

After university, he served as a soldier for two years, but received a medical exemption. In 1941 he joined the

University of Veszprém (now University of Pannonia) for 15 years,[3] where he was the primary developer of the "geometric patterns" theory "of the plane, the sphere and the surface space" and where he "had studied non grid-like structures and quasicrystals" which later became an independent discipline, as reported by János Pach.[8]

The editors of a book dedicated to Fejes Tóth described some highlights of his early work; e.g. having shown that the maximum density of a packing of repeated symmetric convex bodies occurs with a

Freiburg; Madison, Wisconsin; Ohio; and Salzburg.[3]

Fejes Tóth, 1958

Fejes Tóth met his wife in university. She was a chemist. They were parents of three children, two sons—one a professor of mathematics at the Alfréd Rényi Institute of Mathematics, the other a professor of physiology at Dartmouth College—and one daughter, a psychologist.[3] He enjoyed sports, being skilled at table tennis, tennis, and gymnastics. A family photograph shows him swinging by his arms over the top of a high bar when he was around fifty.[8]

Fejes Tóth held the following positions over his career:[2]

  • Assistant instructor, University of Kolozsvár (Cluj) (1941–44)
  • Teacher, Árpád High School (1944–48)
  • Private Lecturer, Pázmány Péter University (1946–48)
  • Professor, University of Veszprém (1949–64)[3]
  • Researcher, then director (in 1970), Mathematical Research Institute (Alfréd Rényi Institute of Mathematics) (1965–83)

In addition to his positions in residence, he was a corresponding member of the

Saxonian Academy of Sciences and Humanities, Akademie der Wissenschaften der DDR,[10]
and of the Braunschweigische Wissenschaftlische Gesellschaft.

Work on regular figures

According to

polyhedra and of regular polytopes
". Todd explains that the treatment includes:

The other section, entitled "Genetics of the Regular Figures", covers a number of special problems, according to Todd. These problems include "packings and coverings of circles in a plane, and ... with tessellations on a sphere" and also problems "in the hyperbolic plane, and in Euclidean space of three or more dimensions." At the time, Todd opined that those problems were "a subject in which there is still much scope for research, and one which calls for considerable ingenuity in approaching its problems".[11]

Honors and recognition

Diagram of hexagonal close packing (left) and cubic close packing (right), as seen from different angles.

Imre Bárány credited Fejes Tóth with several influential proofs in the field of discrete and convex geometry, pertaining to packings and coverings by circles, to convex sets in a plane and to packings and coverings in higher dimensions, including the first correct proof of Thue's theorem. He credits Fejes Tóth, along with Paul Erdős, as having helped to "create the school of Hungarian discrete geometry."[6]

Fejes Tóth's monograph, Lagerungen in der Ebene, auf der Kugel und im Raum,[17][18] which was translated into Russian and Japanese, won him the Kossuth Prize in 1957 and the Hungarian Academy of Sciences membership in 1962.[2][8]

William Edge,[19] another reviewer of Regular Figures,[12] cites Fejes Tóth's earlier work, Lagerungen in der Ebene, auf der Kugel und im Raum,[17] as the foundation of his second chapter in Regular Figures. He emphasized that, at the time of this work, the problem of the upper bound for the density of a packing of equal spheres was still unsolved.

The approach that Fejes Tóth suggested in that work, which translates as "packing [of objects] in a plane, on a sphere and in a space", provided

hexagonal close packing arrangements. Hales used a proof by exhaustion involving the checking of many individual cases, using complex computer calculations.[20][21][22][23][24]

Fejes Tóth received the following prizes:[2]

He received honorary degrees from the University of Salzburg (1991) and the University of Veszprém (1997).

In 2008, a conference was convened in Fejes Tóth's memory in Budapest from June 30 – July 6;[4] it celebrated the term, "Intuitive Geometry", coined by Fejes Tóth to refer to the kind of geometry, which is accessible to the "man in the street". According to the conference organizers, the term encompasses combinatorial geometry, the theory of packing, covering and tiling, convexity, computational geometry, rigidity theory, the geometry of numbers, crystallography and classical differential geometry.

The University of Pannonia administers the László Fejes Tóth Prize (Hungarian: Fejes Tóth László-díj) to recognize "outstanding contributions and development in the field of mathematical sciences".[25] In 2015, the year of Fejes Tóth's centennial birth anniversary, the prize was awarded to Károly Bezdek of the University of Calgary in a ceremony held on 19 June 2015 in Veszprém, Hungary.[26]

Partial bibliography

Fejes Tóth in Vienna, 1987

References

  1. ^ Fejes Tóth, László (1950). "Some packing and covering theorems". Acta Sci. Math. 12A: 62–67.
  2. ^ a b c d Kántor-Varga, T. (2010), "Fejes Tóth László", in Horváth, János (ed.), A Panorama of Hungarian Mathematics in the Twentieth Century, I, New York: Springer, pp. 573–574,
    ISBN 9783540307211
  3. ^ a b c d e f g Hargittai, István (2005). "Interview (with László Fejes Tóth)" (in Hungarian). Hungarian Science. p. 318. Retrieved 2013-11-16.
  4. ^ a b Pach, János; et al. (2008), Intuitive Geometry, in Memoriam László Fejes Tóth, Alfréd Rényi Institute of Mathematics
  5. ^ Katona, G. O. H. (2005), "Laszlo Fejes Toth – Obituary", Studia Scientiarum Mathematicarum Hungarica, 42 (2): 113
  6. ^ a b
    ISBN 9783540307211
  7. ^ Fejes Tóth, László (1935). "Des séries exponentielles de Cauchy".
    Comptes rendus de l'Académie des sciences
     (in French) (200). Paris: 1712–1714.
  8. ^ a b c d e f Pach, János (2005-04-09), "Ötvenévesen a nyújtón—Fejes Tóth László emlékezete", Népszabadság (in Hungarian), archived from the original on 2016-04-14, retrieved 2013-12-06
  9. ^ a b Bárány, Imre; Böröczky, Károly; et al. (2014). Bárány, I.; Böröczky, K.J.; Fejes Tóth, G.; Pach, J (eds.). Geometry - Intuitive, Discrete, and Convex—A Tribute to László Fejes Tóth. Bolyai Society Mathematical Studies. Vol. 24. Berlin: Springer. pp. 7–8.
    ISSN 1217-4696
    .
  10. ^ Staff (2010). "Mitglieder der Vorgängerakademien". Berlin-Brandenburgischen Akademie der Wissenschaften. Retrieved 2018-08-25.
  11. ^
    doi:10.1017/S0013091500026055
  12. ^ a b Fejes Tóth, László (1964), Regular Figures, Oxford: Pergamon Press, p. 339
  13. S2CID 39450175
    .
  14. S2CID 11688453
    .
  15. doi:10.1021/jp206115p
    .
  16. ^ Robert Webb: Stella software http://www.software3d.com/Stella.php
  17. ^
    MR 0057566
  18. doi:10.1090/S0002-9904-1954-09805-1
    .
  19. JSTOR 3612913
  20. MR 1745624
    An elementary exposition of the proof of the Kepler conjecture.
  21. S2CID 123375854
  22. MR 2229657
  23. S2CID 6529590
  24. ISBN 978-1-4614-1128-4
  25. ^ Friedler, Ferenc (2010), Pannon Egyetem Műszaki Informatikai Kar Szervezeti és Működési Rend (in Hungarian), University of Pannonia, pp. 29–30[permanent dead link]
  26. ^ Centre for Computational and Discrete Geometry (2015), Professor Károly Bezdek awarded the László Fejes Tóth Prize, University of Calgary, retrieved 2015-07-08

External links

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