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László Fejes Tóth

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558: 467: 46: 518: 362: 538: 483: 498: 582: 265:, 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. 775: 572:
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
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In 2008, a conference was convened in Fejes Tóth's memory in Budapest from June 30 – July 6; 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
303:) for 15 years, 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 757:
administers the László Fejes Tóth Prize (Hungarian: Fejes Tóth László-díj) to recognize "outstanding contributions and development in the field of mathematical sciences". In 2015, the year of Fejes Tóth's centennial birth anniversary, the prize was awarded to
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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".
377:—and one daughter, a psychologist. 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. 310:
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
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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.
2069: 1652:, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete (in German), vol. LXV, Berlin, New York: 1124:, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete (in German), vol. LXV, Berlin, New York: 338:. By 1953, Fejes Tóth had written dozens of papers devoted to these types of fundamental issues. His distinguished academic career allowed him to travel abroad beyond the 517: 1371: 273: 2064: 2059: 1742: 401: 370: 227: 432:, Fejes Tóth divided the topic into two sections. One, entitled "Systematology of the Regular Figures", develops a theory of "regular and Archimedean 272:, now the Eötvös Loránd University. As a freshman, he developed a generalized solution regarding Cauchy exponential series, which he published in the 537: 629:. 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. 611:, which was translated into Russian and Japanese, won him the Kossuth Prize in 1957 and the Hungarian Academy of Sciences membership in 1962. 369:
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
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The approach that Fejes Tóth suggested in that work, which translates as "packing in a plane, on a sphere and in a space", provided
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Kossuth Prize (1957), State Award (1973), Gauss Bicentennial Medal (1977), and Gold Medal of the Hungarian Academy of Sciences (2002)
1354: 1250: 269: 117: 330:), a regular polytope always has the largest possible volume. He developed a technique that proved Steiner's conjecture for the 596:
by circles, to convex sets in a plane and to packings and coverings in higher dimensions, including the first correct proof of
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credited Fejes Tóth with several influential proofs in the field of discrete and convex geometry, pertaining to packings and
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High School. Between 1946 and 1949 he lectured at Pázmány Péter University and starting in 1949 became a professor at the
223: 614: 523: 45: 291:). It was here that he became interested in packing problems. In 1944, he returned to Budapest to teach mathematics at 262: 2025: 396:
Researcher, then director (in 1970), Mathematical Research Institute (Alfréd Rényi Institute of Mathematics) (1965–83)
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Fejes Tóth, László (1940). "Sur un théorème concernant l'approximation des courbes par des suites de polygones".
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Bárány, Imre; Böröczky, Károly; et al. (2014). Bárány, I.; Böröczky, K.J.; Fejes Tóth, G.; Pach, J (eds.).
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After university, he served as a soldier for two years, but received a medical exemption. In 1941 he joined the
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12 March 1915 – 17 March 2005) was a Hungarian mathematician who specialized in geometry. He proved that a
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Diagram of hexagonal close packing (left) and cubic close packing (right), as seen from different angles.
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O’Toole, P. I.; Hudson, T. S. (2011). "New High-Density Packings of Similarly Sized Binary Spheres".
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in 1998. The Kepler conjecture, named after the 17th-century German mathematician and astronomer
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Fejes Tóth, László (1942). "Das gleichseitige Dreiecksgitter als Lösung von Extremalaufgaben".
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Hyperbolic tessellations, those discrete groups generated by two operations whose product is
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Theorems on packings and coverings of geometrical objects, including the packing of spheres
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to attend international conferences and teach at various universities, including those at
311: 276:—1935. He then received his doctorate at Pázmány Péter University, under the direction of 200: 890:
Fejes Tóth, László (1939). "Über die Approximation konvexer Kurven durch Polygonfolgen".
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Hales, Thomas C.; Ferguson, Samuel P. (2006), "A formulation of the Kepler conjecture",
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Fejes Tóth, László (1986), "Densest packing of translates of the union of two circles",
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Fejes Tóth, László (1942). "Die regulären Polyeder, als Lösungen von Extremalaufgaben".
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involving the checking of many individual cases, using complex computer calculations.
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Heppes, Aladár (1 August 2003). "Some Densest Two-Size Disc Packings in the Plane".
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Fejes Tóth, László (1939). "Two inequalities concerning trigonometric polynomials".
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was shown to be the densest possible planar packing of discs with this size ratio.
1718:, vol. 49, Leicester, England: The Mathematical Gazette, pp. 343–345, 774: 690: 581: 400:
In addition to his positions in residence, he was a corresponding member of the
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Tom Kennedy (2006). "Compact packings of the plane with two sizes of discs".
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Spherical arrangements, including an enumeration of the 32 crystal classes
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Hales, Thomas C. (2006), "Historical overview of the Kepler conjecture",
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Geometry - Intuitive, Discrete, and Convex—A Tribute to László Fejes Tóth
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Fejes Tóth, László (1938). "Über einige Extremumaufgaben bei Polyedern".
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Kántor-Varga, T. (2010), "Fejes Tóth László", in Horváth, János (ed.),
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Fejes Tóth, László (1942). "Über die Fouriersche Reihe der Abkühlung".
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Fejes Tóth, László (1939). "Über zwei Maximumaufgaben bei Polyedern".
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Fejes Tóth, László (1938). "Sur les séries exponentielles de Cauchy".
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Fejes Tóth, László (1971), "Lencsék legsűrűbb elhelyezése a síkban",
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Pannon Egyetem Műszaki Informatikai Kar Szervezeti és Működési Rend
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Fejes Tóth, László (1940). "Eine Bemerkung zur Approximation durch
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Fejes Tóth, László (1935). "Des séries exponentielles de Cauchy".
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Fejes Tóth, László (1935). "Des séries exponentielles de Cauchy".
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Plane Ornaments, including two-dimensional crystallographic groups
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Fejes Tóth, László (1950). "Some packing and covering theorems".
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Fejes Tóth, László (1950). "Some packing and covering theorems".
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Polyhedra, including regular solids and convex Archimedean solids
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Hales, Thomas C. (1994), "The status of the Kepler conjecture",
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An elementary exposition of the proof of the Kepler conjecture.
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A Panorama of Hungarian Mathematics in the Twentieth Century, I
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A Panorama of Hungarian Mathematics in the Twentieth Century, I
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Assistant instructor, University of Kolozsvár (Cluj) (1941–44)
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pattern is the most efficient way to pack centrally symmetric
1962:(in Hungarian), University of Pannonia, 2023, pp. 38–40 1007:
Fejes Tóth, László (1940). "Über einen geometrischen Satz".
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Professor Károly Bezdek awarded the László Fejes Tóth Prize
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Fejes Tóth, László (1940). "Über ein extremales Polyeder".
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Fejes Tóth, László (1939). "Über das Schmiegungspolyeder".
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with three prototiles: a triangle, a square and a hexagon.
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Katona, G. O. H. (2005), "Laszlo Fejes Toth – Obituary",
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in a ceremony held on 19 June 2015 in Veszprém, Hungary.
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Fejes Tóth held the following positions over his career:
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Centre for Computational and Discrete Geometry (2015),
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pattern of packing. He also showed that, of all convex
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Gold Medal of the Hungarian Academy of Sciences (2002)
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In work dedicated to Fejes Tóth, this compact binary
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of given surface area that are equivalent to a given
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Berlin-Brandenburgischen Akademie der Wissenschaften
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Private Lecturer, Pázmány Péter University (1946–48)
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Members of the German Academy of Sciences at Berlin
1337: 1335: 1153:(in German), Budapest: Akadémiai Kiadó, p. 316 159: 151: 137: 129: 124: 111: 106: 94: 78: 55: 36: 2015:Hargittai István beszélgetése Fejes Tóth Lászlóval 1681:Lagerungen in der Ebene, auf der Kugel und im Raum 1650:Lagerungen in der Ebene, auf der Kugel und im Raum 1506: 1504: 1122:Lagerungen in der Ebene, auf der Kugel und im Raum 714:encompasses combinatorial geometry, the theory of 623:Lagerungen in der Ebene, auf der Kugel und im Raum 609:Lagerungen in der Ebene, auf der Kugel und im Raum 142:Lagerungen in der Ebene, auf der Kugel und im Raum 1306:Intuitive Geometry, in Memoriam László Fejes Tóth 412:Braunschweigische Wissenschaftlische Gesellschaft 1935:The Kepler Conjecture: The Hales-Ferguson Proof 1933:Hales, Thomas C.; Ferguson, Samuel P. (2011), 1282:(in Hungarian). Hungarian Science. p. 318 710:(1991) and the University of Veszprém (1997). 440:". Todd explains that the treatment includes: 2046:(High School Mathematics and Physics Journal) 1643: 1641: 625:, as the foundation of his second chapter in 274:proceedings of the French Academy of Sciences 8: 2070:Members of the Hungarian Academy of Sciences 1743:Notices of the American Mathematical Society 644:, says that no arrangement of equally sized 207:on the Euclidean plane (a generalization of 1322:Studia Scientiarum Mathematicarum Hungarica 1298: 1296: 1273: 1271: 1269: 1267: 1265: 1263: 1261: 988:Ann. Scuola Norm. Sup., Pisa, Sci. Fis. Mat 402:Saxonian Academy of Sciences and Humanities 393:Professor, University of Veszprém (1949–64) 2026:Ötvenévesen a nyújtón, F. T. L. emlékezete 1236: 1234: 1232: 1230: 667:Fejes Tóth received the following prizes: 33: 1886: 1842: 1698: 1574: 1427: 1425: 1372:Comptes rendus de l'Académie des sciences 1184: 373:, the other a professor of physiology at 1349:, New York: Springer, pp. 431–441, 1245:, New York: Springer, pp. 573–574, 2040:A geometriai elrendezések diszkrét bája 1478: 1476: 1309:, Alfréd Rényi Institute of Mathematics 1207: 462: 1392: 1390: 1388: 1386: 1384: 1382: 706:He received honorary degrees from the 652:than that of the cubic close packing ( 261:As described in a 1999 interview with 2065:21st-century Hungarian mathematicians 2060:20th-century Hungarian mathematicians 1875:Discrete & Computational Geometry 1831:Discrete & Computational Geometry 1515:, Oxford: Pergamon Press, p. 339 1144:, Oxford: Pergamon Press, p. 339 1046:Math.-naturw. Anz. Ungar. Akad. Wiss. 942:Math.-naturw. Anz. Ungar. Akad. Wiss. 371:Alfréd Rényi Institute of Mathematics 228:Alfréd Rényi Institute of Mathematics 194: 120:, as of 1950 Eötvös Loránd University 7: 1634:http://www.software3d.com/Stella.php 1375:(in French) (200). Paris: 1712–1714. 1280:"Interview (with László Fejes Tóth)" 1088:Math.-naturw. Anz. Ungar. Akad. Wiss 648:filling space has a greater average 600:. He credits Fejes Tóth, along with 387:Teacher, Árpád High School (1944–48) 1608:The Journal of Physical Chemistry C 1563:Discrete and Computational Geometry 1528:Discrete and Computational Geometry 1457:"Mitglieder der Vorgängerakademien" 1173:Discrete and Computational Geometry 621:, cites Fejes Tóth's earlier work, 407:Akademie der Wissenschaften der DDR 133:Discrete and combinatorial geometry 16:Hungarian mathematician (1915–2005) 426:, a reviewer of Fejes Tóth's book 230:(1970-1983). He received both the 226:(from 1962) and a director of the 14: 1303:Pach, János; et al. (2008), 529:Regular star—a concave polyhedron 1716:Regular Figures by L. Fejes Toth 556: 536: 516: 496: 481: 465: 211:, a 2-dimensional analog of the 44: 1700:10.1090/S0002-9904-1954-09805-1 1488:Fejes Toth, L., Regular Figures 1780:The Mathematical Intelligencer 1408:(in Hungarian), archived from 1: 2009:Mathematics Genealogy Project 1632:Robert Webb: Stella software 249:, he laid the foundations of 224:Hungarian Academy of Sciences 215:). He also investigated the 196:[ˈfɛjɛʃˈtoːtˈlaːsloː] 1738:"Cannonballs and honeycombs" 524:Small stellated dodecahedron 31:when mentioning individuals. 1714:Edge, W.L. (October 1965), 1648:Fejes Tóth, László (1953), 1511:Fejes Tóth, László (1964), 1149:Fejes Tóth, László (1965), 1140:Fejes Tóth, László (1964), 1120:Fejes Tóth, László (1953), 1090:(in Hungarian and German). 1048:(in Hungarian and German). 944:(in Hungarian and German). 852:(in Hungarian and French). 831:(in Hungarian and German). 810:(in Hungarian and German). 660:arrangements. Hales used a 636:a basis for a proof of the 2106: 1278:Hargittai, István (2005). 778:Fejes Tóth in Vienna, 1987 18: 1897:10.1007/s00454-005-1211-1 1844:10.1007/s00454-005-1210-2 1736:Hales, Thomas C. (2000), 1585:10.1007/s00454-005-1172-4 1540:10.1007/s00454-003-0007-6 1496:10.1017/S0013091500026055 699:Bicentennial Medal (1977) 547:(A 2-dimensional regular 509:Regular convex polyhedron 173: 102: 43: 607:Fejes Tóth's monograph, 270:Pázmány Péter University 118:Pázmány Péter University 27:. This article uses 19:The native form of this 1985:, University of Calgary 925:10.1112/jlms/s1-14.1.44 658:hexagonal close packing 418:Work on regular figures 285:University of Kolozsvár 222:He was a member of the 50:László Fejes Tóth, 1991 1937:, New York: Springer, 973:. Groningen: 474–476. 967:Compositio Mathematica 898:. Groningen: 456–467. 892:Compositio Mathematica 779: 755:University of Pannonia 732:computational geometry 708:University of Salzburg 617:, another reviewer of 586: 577:Honors and recognition 366: 301:University of Pannonia 297:University of Veszprém 187: 1687:Bull. Amer. Math. Soc 777: 764:University of Calgary 748:differential geometry 683:State Prize (now the 584: 364: 257:Early life and career 770:Partial bibliography 268:Fejes Tóth attended 2013:Hungarian Science: 913:J. London Math. Soc 740:geometry of numbers 662:proof by exhaustion 654:face-centered cubic 107:Academic background 1793:10.1007/BF03024356 1186:10.1007/bf02187703 1021:10.1007/bf01181430 780: 587: 490:packing of spheres 367: 348:Madison, Wisconsin 29:Western name order 2005:László Fejes Tóth 1944:978-1-4614-1128-4 1683:by L. Fejes Tóth" 1675:Coxeter, H. S. M. 1620:10.1021/jp206115p 1160:Matematikai Lapok 638:Kepler conjecture 459:Regular polytopes 438:regular polytopes 375:Dartmouth College 251:discrete geometry 213:Kepler conjecture 188:Fejes Tóth László 180:László Fejes Tóth 177: 176: 89:Budapest, Hungary 38:László Fejes Tóth 25:Fejes Tóth László 2097: 2019:Magyar Tudomány, 1993: 1992: 1991: 1990: 1976: 1970: 1969: 1968: 1967: 1954: 1948: 1947: 1930: 1924: 1923: 1890: 1870: 1864: 1863: 1846: 1826: 1820: 1819: 1774: 1768: 1766: 1733: 1727: 1726: 1711: 1705: 1704: 1702: 1671: 1665: 1664: 1645: 1636: 1630: 1624: 1623: 1603: 1597: 1596: 1578: 1558: 1552: 1551: 1523: 1517: 1516: 1508: 1499: 1498: 1480: 1471: 1470: 1468: 1467: 1452: 1446: 1445: 1429: 1420: 1419: 1418: 1417: 1394: 1377: 1376: 1366: 1360: 1359: 1339: 1330: 1329: 1317: 1311: 1310: 1300: 1291: 1290: 1288: 1287: 1275: 1256: 1255: 1238: 1225: 1224: 1212: 1197: 1188: 1167: 1154: 1151:Reguläre Figuren 1145: 1136: 1116: 1103: 1082: 1061: 1040: 1003: 982: 957: 936: 907: 886: 865: 844: 823: 802: 787:C. R. Acad. Sci. 560: 540: 520: 500: 485: 469: 365:Fejes Tóth, 1958 263:István Hargittai 198: 193: 85: 69: 67: 48: 34: 2105: 2104: 2100: 2099: 2098: 2096: 2095: 2094: 2050: 2049: 2001: 1996: 1988: 1986: 1978: 1977: 1973: 1965: 1963: 1956: 1955: 1951: 1945: 1932: 1931: 1927: 1872: 1871: 1867: 1828: 1827: 1823: 1776: 1775: 1771: 1735: 1734: 1730: 1713: 1712: 1708: 1673: 1672: 1668: 1656:, p. 238, 1654:Springer-Verlag 1647: 1646: 1639: 1631: 1627: 1605: 1604: 1600: 1560: 1559: 1555: 1525: 1524: 1520: 1513:Regular Figures 1510: 1509: 1502: 1482: 1481: 1474: 1465: 1463: 1454: 1453: 1449: 1431: 1430: 1423: 1415: 1413: 1396: 1395: 1380: 1368: 1367: 1363: 1357: 1341: 1340: 1333: 1319: 1318: 1314: 1302: 1301: 1294: 1285: 1283: 1277: 1276: 1259: 1253: 1240: 1239: 1228: 1214: 1213: 1209: 1205: 1200: 1170: 1157: 1148: 1142:Regular Figures 1139: 1128:, p. 238, 1126:Springer-Verlag 1119: 1106: 1085: 1067:Mat. Fiz. Lapok 1064: 1043: 1006: 985: 960: 939: 910: 889: 871:Tôhoku Math. J. 868: 850:Mat. Fiz. Lapok 847: 829:Mat. Fiz. Lápok 826: 808:Mat. Fiz. Lapok 805: 784: 772: 744:crystallography 736:rigidity theory 685:Széchenyi Prize 642:Johannes Kepler 627:Regular Figures 619:Regular Figures 579: 568: 563:A semi-regular 561: 552: 546: 541: 532: 526: 521: 512: 506: 501: 492: 486: 477: 470: 429:Regular Figures 420: 259: 191: 146:Regular Figures 90: 87: 83: 74: 73:Szeged, Hungary 71: 65: 63: 62: 61: 51: 39: 32: 17: 12: 11: 5: 2103: 2101: 2093: 2092: 2087: 2082: 2077: 2072: 2067: 2062: 2052: 2051: 2048: 2047: 2036: 2035:April 9, 2005. 2022: 2011: 2000: 1999:External links 1997: 1995: 1994: 1971: 1949: 1943: 1925: 1865: 1821: 1769: 1750:(4): 440–449, 1728: 1706: 1693:(2): 202–206. 1666: 1637: 1625: 1598: 1569:(2): 255–267. 1553: 1534:(2): 241–262. 1518: 1500: 1472: 1455:Staff (2010). 1447: 1421: 1400:(2005-04-09), 1378: 1361: 1355: 1331: 1312: 1292: 1257: 1251: 1226: 1217:Acta Sci. Math 1206: 1204: 1201: 1199: 1198: 1179:(4): 307–314, 1168: 1155: 1146: 1137: 1117: 1109:Acta Sci. Math 1104: 1083: 1062: 1041: 1004: 994:(9): 143–145. 983: 958: 937: 908: 887: 866: 845: 824: 803: 781: 771: 768: 746:and classical 704: 703: 700: 694: 688: 681: 675: 598:Thue's theorem 578: 575: 570: 569: 562: 555: 553: 542: 535: 533: 522: 515: 513: 502: 495: 493: 487: 480: 478: 474:circle packing 471: 464: 461: 460: 457: 454: 448: 445: 419: 416: 398: 397: 394: 391: 388: 385: 320:Platonic solid 258: 255: 243:H.S.M. Coxeter 241:Together with 217:sphere packing 209:Thue's theorem 175: 174: 171: 170: 161: 157: 156: 153: 149: 148: 139: 135: 134: 131: 130:Main interests 127: 126: 122: 121: 115: 109: 108: 104: 103: 100: 99: 96: 92: 91: 88: 86:(aged 90) 80: 76: 75: 72: 59: 57: 53: 52: 49: 41: 40: 37: 15: 13: 10: 9: 6: 4: 3: 2: 2102: 2091: 2088: 2086: 2083: 2081: 2078: 2076: 2073: 2071: 2068: 2066: 2063: 2061: 2058: 2057: 2055: 2045: 2041: 2037: 2034: 2032: 2027: 2023: 2020: 2016: 2012: 2010: 2006: 2003: 2002: 1998: 1984: 1983: 1975: 1972: 1961: 1960: 1953: 1950: 1946: 1940: 1936: 1929: 1926: 1922: 1918: 1914: 1910: 1906: 1902: 1898: 1894: 1889: 1884: 1880: 1876: 1869: 1866: 1862: 1858: 1854: 1850: 1845: 1840: 1836: 1832: 1825: 1822: 1818: 1814: 1810: 1806: 1802: 1798: 1794: 1790: 1786: 1782: 1781: 1773: 1770: 1765: 1761: 1757: 1753: 1749: 1745: 1744: 1739: 1732: 1729: 1725: 1721: 1717: 1710: 1707: 1701: 1696: 1692: 1688: 1684: 1682: 1676: 1670: 1667: 1663: 1659: 1655: 1651: 1644: 1642: 1638: 1635: 1629: 1626: 1621: 1617: 1614:(39): 19037. 1613: 1609: 1602: 1599: 1594: 1590: 1586: 1582: 1577: 1572: 1568: 1564: 1557: 1554: 1549: 1545: 1541: 1537: 1533: 1529: 1522: 1519: 1514: 1507: 1505: 1501: 1497: 1493: 1489: 1485: 1479: 1477: 1473: 1462: 1458: 1451: 1448: 1443: 1439: 1435: 1428: 1426: 1422: 1412:on 2016-04-14 1411: 1407: 1403: 1399: 1393: 1391: 1389: 1387: 1385: 1383: 1379: 1374: 1373: 1365: 1362: 1358: 1356:9783540307211 1352: 1348: 1344: 1338: 1336: 1332: 1327: 1323: 1316: 1313: 1308: 1307: 1299: 1297: 1293: 1281: 1274: 1272: 1270: 1268: 1266: 1264: 1262: 1258: 1254: 1252:9783540307211 1248: 1244: 1237: 1235: 1233: 1231: 1227: 1222: 1218: 1211: 1208: 1202: 1196: 1192: 1187: 1182: 1178: 1174: 1169: 1165: 1161: 1156: 1152: 1147: 1143: 1138: 1135: 1131: 1127: 1123: 1118: 1114: 1110: 1105: 1101: 1097: 1093: 1089: 1084: 1080: 1076: 1072: 1068: 1063: 1059: 1055: 1051: 1047: 1042: 1038: 1034: 1030: 1026: 1022: 1018: 1014: 1011:(in German). 1010: 1005: 1001: 997: 993: 990:(in French). 989: 984: 980: 976: 972: 969:(in German). 968: 964: 959: 955: 951: 947: 943: 938: 934: 930: 926: 922: 918: 914: 909: 905: 901: 897: 894:(in German). 893: 888: 884: 880: 876: 873:(in German). 872: 867: 863: 859: 855: 851: 846: 842: 838: 834: 830: 825: 821: 817: 813: 809: 804: 800: 796: 793:: 1712–1714. 792: 789:(in French). 788: 783: 782: 776: 769: 767: 765: 761: 760:Károly Bezdek 756: 751: 749: 745: 741: 737: 733: 729: 725: 721: 717: 711: 709: 701: 698: 695: 692: 689: 686: 682: 679: 678:Kossuth Prize 676: 673: 670: 669: 668: 665: 663: 659: 655: 651: 647: 643: 639: 635: 630: 628: 624: 620: 616: 612: 610: 605: 603: 599: 595: 591: 583: 576: 574: 566: 559: 554: 550: 545: 539: 534: 530: 525: 519: 514: 510: 505: 499: 494: 491: 484: 479: 475: 468: 463: 458: 455: 453: 449: 446: 443: 442: 441: 439: 435: 431: 430: 425: 422:According to 417: 415: 413: 410:, and of the 409: 408: 403: 395: 392: 389: 386: 383: 382: 381: 378: 376: 372: 363: 359: 357: 353: 349: 345: 341: 337: 333: 329: 325: 321: 317: 313: 308: 306: 302: 298: 294: 290: 286: 281: 279: 275: 271: 266: 264: 256: 254: 252: 248: 244: 239: 237: 233: 232:Kossuth Prize 229: 225: 220: 218: 214: 210: 206: 202: 197: 189: 185: 181: 172: 169: 168:Károly Bezdek 165: 162: 158: 154: 152:Notable ideas 150: 147: 143: 140: 138:Notable works 136: 132: 128: 125:Academic work 123: 119: 116: 114: 110: 105: 101: 97: 93: 82:17 March 2005 81: 77: 70:12 March 1915 58: 54: 47: 42: 35: 30: 26: 22: 21:personal name 2043: 2038:János Pach: 2031:Népszabadság 2029: 2024:János Pach: 2021:March, 2005. 2018: 1987:, retrieved 1981: 1974: 1964:, retrieved 1958: 1952: 1934: 1928: 1888:math/9811078 1881:(1): 21–69, 1878: 1874: 1868: 1834: 1830: 1824: 1787:(3): 47–58, 1784: 1778: 1772: 1747: 1741: 1731: 1715: 1709: 1690: 1686: 1680: 1669: 1649: 1628: 1611: 1607: 1601: 1576:math/0407145 1566: 1562: 1556: 1531: 1527: 1521: 1512: 1487: 1464:. Retrieved 1460: 1450: 1433: 1414:, retrieved 1410:the original 1406:Népszabadság 1405: 1370: 1364: 1346: 1343:Bárány, Imre 1325: 1321: 1315: 1305: 1284:. Retrieved 1242: 1220: 1216: 1210: 1176: 1172: 1163: 1159: 1150: 1141: 1121: 1112: 1108: 1091: 1087: 1070: 1066: 1049: 1045: 1012: 1008: 991: 987: 970: 966: 965:-Eckringe". 962: 945: 941: 916: 912: 895: 891: 874: 870: 853: 849: 832: 828: 811: 807: 790: 786: 752: 712: 705: 693:Prize (1977) 674:Prize (1943) 666: 634:Thomas Hales 631: 626: 622: 618: 615:William Edge 613: 608: 606: 588: 571: 565:tessellation 504:Dodecahedron 427: 421: 411: 405: 399: 379: 368: 340:Iron Curtain 336:dodecahedron 334:and for the 309: 282: 267: 260: 240: 221: 179: 178: 164:Thomas Hales 145: 141: 84:(2005-03-17) 24: 2085:2005 deaths 2080:1915 births 1837:(1): 5–20, 1398:Pach, János 1094:: 478–495. 1073:: 238–248. 1052:: 471–477. 948:: 476–479. 856:: 115–132. 835:: 141–145. 814:: 191–199. 691:Tibor Szele 590:Imre Bárány 324:tetrahedron 278:Lipót Fejér 236:State Award 234:(1957) and 205:convex sets 60:László Tóth 2054:Categories 1989:2015-07-08 1966:2024-06-17 1484:Todd, J.A. 1466:2018-08-25 1416:2013-12-06 1286:2013-11-16 1203:References 1195:0606.52004 1100:68.0144.03 1079:68.0340.04 1058:68.0341.02 1029:66.0902.03 1000:66.0902.04 979:66.0902.05 954:66.0905.04 933:65.0254.01 904:65.0822.03 883:65.0826.03 862:64.0284.04 841:65.0827.01 820:64.0732.02 799:62.1191.03 672:Klug Lipót 602:Paul Erdős 452:involutary 424:J. A. Todd 328:octahedron 305:János Pach 247:Paul Erdős 192:pronounced 160:Influenced 113:Alma mater 66:1915-03-12 2075:Geometers 1905:0179-5376 1853:0179-5376 1817:123375854 1801:0343-6993 1756:0002-9920 1679:"Review: 1442:1217-4696 1166:: 209–213 1037:121092302 1015:: 83–85. 919:: 44–46. 877:: 79–83. 728:convexity 594:coverings 434:polyhedra 316:polytopes 184:Hungarian 1677:(1954). 1593:11688453 1548:39450175 1486:(1964), 1328:(2): 113 1223:: 62–67. 1115:: 62–67. 1009:Math. Z. 720:covering 687:) (1973) 549:polytope 544:Heptagon 488:A dense 356:Salzburg 344:Freiburg 322:(e.g. a 238:(1973). 2007:at the 1921:6529590 1913:2229658 1861:2229657 1809:1281754 1764:1745624 1724:3612913 1662:0057566 1134:0057566 762:of the 716:packing 650:density 646:spheres 436:and of 312:lattice 201:lattice 1941:  1919:  1911:  1903:  1859:  1851:  1815:  1807:  1799:  1762:  1754:  1722:  1660:  1591:  1546:  1440:  1353:  1249:  1193:  1132:  1098:  1077:  1056:  1035:  1027:  998:  977:  952:  931:  902:  881:  860:  839:  818:  797:  738:, the 724:tiling 680:(1957) 656:) and 354:; and 326:or an 95:Awards 2044:KöMaL 1917:S2CID 1883:arXiv 1813:S2CID 1720:JSTOR 1589:S2CID 1571:arXiv 1544:S2CID 1033:S2CID 697:Gauss 299:(now 293:Árpád 1939:ISBN 1901:ISSN 1849:ISSN 1797:ISSN 1752:ISSN 1438:ISSN 1351:ISBN 1247:ISBN 753:The 722:and 352:Ohio 332:cube 289:Cluj 245:and 79:Died 56:Born 1893:doi 1839:doi 1789:doi 1695:doi 1616:doi 1612:115 1581:doi 1536:doi 1492:doi 1221:12A 1191:Zbl 1181:doi 1113:12A 1096:JFM 1075:JFM 1054:JFM 1025:JFM 1017:doi 996:JFM 975:JFM 950:JFM 929:JFM 921:doi 900:JFM 879:JFM 858:JFM 837:JFM 816:JFM 795:JFM 791:200 23:is 2056:: 2028:, 2017:, 1915:, 1909:MR 1907:, 1899:, 1891:, 1879:36 1877:, 1857:MR 1855:, 1847:, 1835:36 1833:, 1811:, 1805:MR 1803:, 1795:, 1785:16 1783:, 1760:MR 1758:, 1748:47 1746:, 1740:, 1691:60 1689:. 1685:. 1658:MR 1640:^ 1610:. 1587:. 1579:. 1567:35 1565:. 1542:. 1532:30 1530:. 1503:^ 1475:^ 1459:. 1424:^ 1404:, 1381:^ 1334:^ 1326:42 1324:, 1295:^ 1260:^ 1229:^ 1219:. 1189:, 1175:, 1164:22 1162:, 1130:MR 1111:. 1092:61 1071:49 1069:. 1050:61 1031:. 1023:. 1013:46 946:59 927:. 917:14 915:. 875:46 854:45 833:46 812:45 750:. 742:, 734:, 730:, 726:, 718:, 414:. 404:, 358:. 350:; 346:; 307:. 280:. 253:. 190:, 186:: 166:, 144:; 2033:, 1895:: 1885:: 1841:: 1791:: 1703:. 1697:: 1622:. 1618:: 1595:. 1583:: 1573:: 1550:. 1538:: 1494:: 1469:. 1444:. 1289:. 1183:: 1177:1 1102:. 1081:. 1060:. 1039:. 1019:: 1002:. 992:2 981:. 971:7 963:n 956:. 935:. 923:: 906:. 896:6 885:. 864:. 843:. 822:. 801:. 551:) 531:) 527:( 511:) 507:( 287:( 182:( 68:) 64:(

Index

personal name
Western name order

Alma mater
Pázmány Péter University
Thomas Hales
Károly Bezdek
Hungarian
[ˈfɛjɛʃˈtoːtˈlaːsloː]
lattice
convex sets
Thue's theorem
Kepler conjecture
sphere packing
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
Kossuth Prize
State Award
H.S.M. Coxeter
Paul Erdős
discrete geometry
István Hargittai
Pázmány Péter University
proceedings of the French Academy of Sciences
Lipót Fejér
University of Kolozsvár
Cluj
Árpád
University of Veszprém
University of Pannonia

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