429:
894:
1880:
324:, and his older brother, Hertvík Jarník, also became a professor of linguistics. Despite this background, Jarník learned no Latin at his gymnasium (the C.K. české vyšší reálné gymnasium, Ječná, Prague), so when he entered Charles University in 1915 he had to do so as an extraordinary student until he could pass a Latin examination three semesters later.
790:
44:
1680:. See in particular page 127: "Soon after Borůvka's published his solution, another Czech mathematician, Vojtěch Jarník, reacted by publishing his own solution," and page 133: "Jarník’s article on this topic is an extract from a letter to O. Borůvka".
354:, and on his return from the second visit, he was given a chair in mathematics as an extraordinary professor. He was promoted to full professor in 1935 and later served as Dean of Sciences (1947–1948) and Vice-Rector (1950–1953). He retired in 1968.
780:
of functions) are nowhere differentiable, Jarník proved that at almost all points, all four Dini derivatives of such a function are infinite. Much of his later work in this area concerned extensions of these results to approximate derivatives.
874:. However, additional points that are not part of the input may be added to make the overall tree shorter. This paper is the first serious treatment of the general Steiner tree problem (although it appears earlier in a letter by
274:. He has been called "probably the first Czechoslovak mathematician whose scientific works received wide and lasting international response". As well as developing Jarník's algorithm, he found tight bounds on the number of
693:
548:
1582:
Beresnevich, Victor; Ramírez, Felipe; Velani, Sanju (2016), "Metric
Diophantine approximation: Aspects of recent work", in Badziahin, Dzmitry; Gorodnik, Alexander; Peyerimhoff, Norbert (eds.),
886:
Jarník was a member of the Czech
Academy of Sciences and Arts, from 1934 as an extraordinary member and from 1946 as a regular member. In 1952 he became one of the founding members of
940:
764:
is infinite. This applies in particular to the nowhere-differentiable functions, as they must have unbounded variation in all intervals. Later, after learning of a result by
615:
one. This is the same dimension as the set of all real numbers, intuitively suggesting that the set of badly approximable numbers is large. He also considered the numbers
840:
by repeatedly adding the cheapest connection to any other vertex, until all vertices have been connected. The same algorithm was later rediscovered in the late 1950s by
1920:
571:
1844:
1786:
1637:
1558:
1311:
918:
748:, previously considered to be the first example of such a function. Based on his study of Bolzano's function, Jarník was led to a more general theorem: If a
1352:
1690:
1915:
635:
1910:
350:
at the
University of Göttingen from 1923 to 1925 and again from 1927 to 1929. On his first return to Charles University he defended his
1925:
720:. Besicovitch used different methods than Jarník to prove it, and the result has come to be known as the Jarník–Besicovitch theorem.
1852:
1794:
1704:
1674:
1645:
1566:
1528:
1501:
1474:
1319:
887:
466:
248:
370:
1418:
717:
584:
Another theorem of Jarník in this area shows that, for any closed convex curve in the plane with a well-defined length, the
1884:
1389:
332:
878:), and it already contains "virtually all general properties of Steiner trees" later attributed to other researchers.
987:. A function with unbounded variation in all intervals has a dense set of points where a Dini derivative is infinite.
809:
417:
997:
592:
581:
nor the leading constant of this bound can be improved, as there exist convex curves with this many grid points.
405:
287:
118:
825:
1763:
1357:
833:
794:
252:
129:
1586:, London Mathematical Society Lecture Note Series, vol. 437, Cambridge University Press, pp. 1–95,
870:. In this problem, one must again form a tree connecting a given set of points, with edge costs given by the
1413:
1065:
741:
1613:. See Theorem 1.33 (the Jarník–Besicovitch theorem), p. 23, and the discussion following the theorem.
1209:
1205:
817:
798:
428:
393:
267:
256:
134:
1101:
303:
1905:
1900:
1193:
875:
867:
749:
745:
437:
401:
291:
1343:
852:
769:
737:
612:
585:
413:
358:
283:
199:
893:
1605:
1587:
1022:
871:
845:
608:
588:
between the area it encloses and the number of integer points it encloses is at most its length.
321:
244:
164:
1347:
1848:
1790:
1700:
1694:
1670:
1641:
1562:
1524:
1518:
1497:
1470:
1464:
1315:
1201:
1030:. Tight bounds on the number of integer points on a convex curve, as a function of its length.
829:
757:
378:
374:
366:
339:. In 1921 he completed a doctoral degree (RNDr.) at Charles University with a dissertation on
308:
209:
204:
1491:
857:
1597:
1435:
1427:
1304:
Veselý, Jiří (1999), "Pedagogical activities of Vojtěch Jarník", in Novák, Břetislav (ed.),
1262:
1184:
1174:
1141:
1131:
1121:
1074:
1047:
1006:
979:
969:
926:
805:
773:
760:
in any subinterval, then there is a dense subset of its domain on which at least one of its
314:
171:
1449:
1018:
1445:
1188:
1145:
1078:
1051:
1014:
983:
906:
761:
753:
733:
600:
441:
409:
340:
271:
72:
43:
1496:, London Mathematical Society Monographs, vol. 13, Clarendon Press, pp. 31–33,
901:
The Vojtěch Jarník
International Mathematical Competition, held each year since 1991 in
331:
as a mentor. After completing his studies, he became an assistant to Jan Vojtěch at the
1409:
922:
841:
837:
574:
556:
232:
105:
94:
1431:
932:
A conference was held in Prague, in March 1998, to honor the centennial of his birth.
1894:
1609:
1026:
914:
765:
729:
397:
357:
Jarník supervised the dissertations of 16 doctoral students. Notable among these are
347:
336:
275:
263:
240:
186:
123:
1247:
453:
362:
351:
279:
1154:
897:
Jarníkova Street, the Jarníkova bus stop, and a commemorative sign honoring Jarník
1584:
Dynamics and
Analytic Number Theory: Proceedings of the Durham Easter School 2014
607:) that the badly approximable real numbers (the ones with bounded terms in their
392:
Although Jarník's 1921 dissertation, like some of his later publications, was in
327:
He studied mathematics and physics at
Charles University from 1915 to 1919, with
596:
154:
1779:
Novák, Břetislav, ed. (1999), "Bibliography of scientific works of V. Jarník",
1601:
1440:
1179:
1136:
974:
777:
328:
176:
17:
1463:
Bordellès, Olivier (2012), "5.4.7 Counting integer points on smooth curves",
343:
supervised by Petr, then returned to
Charles University as Petr's assistant.
1385:
1266:
813:
317:
1879:
1862:
1838:
1126:
1087:
1060:
1035:
917:
published by
Czechoslovakia in 1987 to honor the 125th anniversary of the
1376:; however, O'Connor and Robertson give his return dates as 1924 and 1928.
1090:[About a certain minimal problem (from a letter to O. Borůvka)],
1743:
1149:. Generic functions have infinite Dini derivatives at almost all points.
789:
1082:. The well-approximable numbers have Hausdorff dimension less than one.
1010:
902:
848:. It is also known as Prim's algorithm or the Prim–Dijkstra algorithm.
68:
1551:"Some recent extensions of Jarník's work in Diophantine approximation"
1212:. These books "became classics for several generations of students".
910:
445:
237:
90:
64:
1592:
688:{\displaystyle \left|x-{\frac {p}{q}}\right|<{\frac {1}{q^{k}}}}
619:
for which there exist infinitely many good rational approximations
892:
788:
427:
346:
While keeping his position at
Charles University, he studied with
960:[On derivative numbers of functions of a real variable],
744:. Bolzano's 1830 discovery predated the 1872 publication of the
416:. He also made pioneering, but long-neglected, contributions to
1416:(2001). "Vojtěch Jarník's work in combinatorial optimization".
1248:"In memoriam Prof. Vojtěch Jarník (22. 12. 1897 – 22. 9. 1970)"
1063:[Diophantine approximation and the Hausdorff measure],
992:
243:. He worked for many years as a professor and administrator at
1520:
Number Theory: An
Introduction to Pure and Applied Mathematics
1055:. The badly-approximable numbers have Hausdorff dimension one.
1038:[On the metric theory of Diophantine approximations],
1780:
1669:, Prague: Výzkumné centrum pro dějiny vědy, pp. 51–184,
1662:
1629:
1550:
1305:
1109:
957:
1112:[On the differentiability of continuous functions],
1088:"O jistém problému minimálním. (Z dopisu panu O. Borůvkovi)"
890:. He was also awarded the Czechoslovak State Prize in 1952.
1036:"Zur metrischen Theorie der diophantischen Approximationen"
543:{\displaystyle {\frac {3}{\sqrt{2\pi }}}L^{2/3}+O(L^{1/3})}
1810:
1699:(4th ed.). Addison-Wesley Professional. p. 628.
716:. The second of these results was later rediscovered by
452:), related to this problem, is that any closed strictly
1722:"Vojtěch Jarník International Mathematical Competition"
1721:
905:, is named in his honor, as is Jarníkova Street in the
836:
builds a tree from a single starting vertex of a given
302:
Jarník was born on 22 December 1897. He was the son of
1061:"Diophantische Approximationen und Hausdorffsches Maß"
951:
Jarník published 90 papers in mathematics, including:
941:
Faculty of Mathematics and Physics, Charles University
1200:
He was also the author of ten textbooks in Czech, on
958:"O číslech derivovaných funkcí jedné reálné proměnné"
638:
559:
469:
732:
was sparked by finding, in the unpublished works of
919:
Union of Czechoslovak mathematicians and physicists
192:
182:
170:
160:
150:
111:
101:
79:
50:
34:
1110:"Über die Differenzierbarkeit stetiger Funktionen"
921:included one stamp featuring Jarník together with
709:) that these have the smaller Hausdorff dimension
687:
565:
542:
286:of sets of real numbers and how well they can be
851:He also published a second, related, paper with
432:A convex curve through 13 integer lattice points
384:He died on 22 September 1970, at the age of 72.
1630:"The work of Professor Jarník in real analysis"
995:[On the grid points on convex curves],
1490:Huxley, M. N. (1996), "2.2 Jarník's polygon",
236:; 22 December 1897 – 22 September 1970) was a
863:
8:
1845:Union of Czech mathematicians and physicists
1787:Union of Czech mathematicians and physicists
1744:"Images of Mathematicians on Postage Stamps"
1638:Union of Czech mathematicians and physicists
1559:Union of Czech mathematicians and physicists
1312:Union of Czech mathematicians and physicists
993:"Über die Gitterpunkte auf konvexen Kurven"
604:
1493:Area, Lattice Points, and Exponential Sums
42:
31:
1815:, Czech Digital Mathematics Library, 2010
1623:
1621:
1619:
1591:
1544:
1542:
1540:
1439:
1178:
1167:Časopis pro Pěstování Matematiky a Fysiky
1135:
1125:
1092:Práce Moravské Přírodovědecké Společnosti
973:
962:Časopis Pro Pěstování Matematiky a Fysiky
677:
668:
650:
637:
591:Jarník also published several results in
558:
527:
523:
500:
496:
484:
470:
468:
365:who became rector of Charles University,
1667:Mathematics Throughout the Ages, Vol. II
1404:
1402:
1400:
1398:
1241:
1239:
1237:
1235:
1233:
1231:
1229:
1227:
1225:
1153:Jarník, Vojtěch; Kössler, Miloš (1934),
1353:MacTutor History of Mathematics Archive
1280:
1221:
282:, studied the relationship between the
1774:
1772:
1373:
1369:
821:
706:
449:
1299:
1297:
1295:
1293:
1291:
1289:
1192:. The first serious treatment of the
1155:"O minimálních grafech, obsahujících
943:, in a lecture hall named after him.
440:asks for the number of points of the
290:, and investigated the properties of
231:
7:
1921:Academic staff of Charles University
1663:"A history of discrete optimization"
1337:
1335:
1333:
1331:
824:, in response to the publication of
595:, the study of the approximation of
1867:, Czech Digital Mathematics Library
553:points of the integer lattice. The
1161:[On minimal graphs containing
573:in this formula is an instance of
404:and proved a number of results on
25:
1878:
888:Czechoslovak Academy of Sciences
828:by another Czech mathematician,
292:nowhere-differentiable functions
288:approximated by rational numbers
249:Czechoslovak Academy of Sciences
1840:Life and work of Vojtěch Jarník
1782:Life and work of Vojtěch Jarník
1634:Life and work of Vojtěch Jarník
1555:Life and work of Vojtěch Jarník
1307:Life and work of Vojtěch Jarník
396:, his main area of work was in
1864:Vojtěch Jarník digital archive
1837:Novák, Břetislav, ed. (1999),
537:
516:
1:
1632:, in Novák, Břetislav (ed.),
1553:, in Novák, Břetislav (ed.),
1432:10.1016/S0012-365X(00)00256-9
1390:Mathematics Genealogy Project
1100:. The original reference for
1034:Jarník, Vojtĕch (1928–1929),
333:Brno University of Technology
448:. One of Jarník's theorems (
183:Other academic advisors
1916:Czechoslovak mathematicians
1104:for minimum spanning trees.
1040:Prace Matematyczno-Fizyczne
776:(that is, the members of a
377:, and Slovak mathematician
1942:
1911:Mathematicians from Prague
1665:, in Fuchs, Eduard (ed.),
1523:, CRC Press, p. 561,
810:combinatorial optimization
785:Combinatorial optimization
577:. Neither the exponent of
418:combinatorial optimization
371:Henstock–Kurzweil integral
1926:Charles University alumni
1602:10.1017/9781316402696.002
1469:, Springer, p. 290,
1180:10.21136/CPMF.1934.122548
998:Mathematische Zeitschrift
975:10.21136/CPMF.1924.109353
812:, Jarník is known for an
593:Diophantine approximation
406:Diophantine approximation
233:[ˈvojcɛxˈjarɲiːk]
218:
143:
119:Diophantine approximation
41:
1661:Durnová, Helena (2004),
1358:University of St Andrews
1108:Jarník, Vojtěch (1933),
1086:Jarník, Vojtěch (1930),
1059:Jarník, Vojtĕch (1929),
991:Jarník, Vojtěch (1926),
956:Jarník, Vojtěch (1923),
373:, Czech number theorist
251:. He is the namesake of
1693:; Wayne, Kevin (2011).
1267:10.21136/MB.1998.126302
1114:Fundamenta Mathematicae
1066:Matematicheskii Sbornik
935:Since 2002, ceremonial
460:passes through at most
247:, and helped found the
1628:Preiss, David (1999),
1549:Dodson, M. M. (1999),
1206:differential equations
939:is held every year at
898:
882:Recognition and legacy
818:minimum spanning trees
801:
799:minimum spanning trees
689:
567:
544:
433:
257:minimum spanning trees
1517:Redmond, Don (1996),
1246:Netuka, Ivan (1998).
1210:mathematical analysis
1127:10.4064/fm-21-1-48-58
947:Selected publications
896:
792:
724:Mathematical analysis
698:for a given exponent
690:
568:
545:
431:
394:mathematical analysis
268:mathematical analysis
135:Mathematical analysis
1887:at Wikimedia Commons
1789:, pp. 133–142,
1419:Discrete Mathematics
1344:Robertson, Edmund F.
1255:Mathematica Bohemica
1194:Steiner tree problem
1046:, Warszawa: 91–106,
868:Steiner tree problem
750:real-valued function
746:Weierstrass function
736:, a definition of a
636:
557:
467:
444:enclosed by a given
438:Gauss circle problem
402:Gauss circle problem
335:, where he also met
298:Education and career
229:Czech pronunciation:
1764:Ceremonial Lectures
1342:O'Connor, John J.;
1165:given points],
866:) on the Euclidean
826:Borůvka's algorithm
770:Stefan Mazurkiewicz
738:continuous function
613:Hausdorff dimension
609:continued fractions
586:absolute difference
414:geometry of numbers
284:Hausdorff dimension
27:Czech mathematician
1640:, pp. 55–66,
1561:, pp. 23–36,
1441:10338.dmlcz/500662
1414:Nešetřil, Jaroslav
1314:, pp. 83–94,
1253:. News and Notes.
1137:10338.dmlcz/500736
1102:Jarnik's algorithm
1011:10.1007/BF01216795
899:
872:Euclidean distance
846:Edsger W. Dijkstra
834:Jarník's algorithm
802:
795:Jarník's algorithm
685:
563:
540:
434:
412:problems, and the
322:Charles University
253:Jarník's algorithm
245:Charles University
165:Charles University
130:Jarník's algorithm
1883:Media related to
1691:Sedgewick, Robert
1202:integral calculus
822:published in 1930
816:for constructing
774:generic functions
758:bounded variation
740:that was nowhere
728:Jarník's work in
683:
658:
566:{\displaystyle O}
490:
489:
400:. He studied the
367:Jaroslav Kurzweil
313:, a professor of
262:Jarník worked in
222:
221:
205:Jaroslav Kurzweil
193:Doctoral students
145:Scientific career
83:22 September 1970
16:(Redirected from
1933:
1882:
1868:
1857:
1824:
1822:
1821:
1820:
1807:
1801:
1799:
1776:
1767:
1761:
1755:
1753:
1751:
1750:
1739:
1733:
1732:
1730:
1728:
1718:
1712:
1710:
1687:
1681:
1679:
1658:
1652:
1650:
1625:
1614:
1612:
1595:
1579:
1573:
1571:
1546:
1535:
1533:
1514:
1508:
1506:
1487:
1481:
1479:
1466:Arithmetic Tales
1460:
1454:
1453:
1443:
1406:
1393:
1383:
1377:
1367:
1361:
1360:
1348:"Vojtěch Jarník"
1339:
1326:
1324:
1301:
1284:
1278:
1272:
1270:
1252:
1243:
1191:
1182:
1164:
1158:
1148:
1139:
1129:
1099:
1081:
1054:
1029:
986:
977:
937:Jarník's lecture
927:Vincenc Strouhal
861:
806:computer science
762:Dini derivatives
715:
704:
694:
692:
691:
686:
684:
682:
681:
669:
664:
660:
659:
651:
628:
618:
601:rational numbers
580:
572:
570:
569:
564:
549:
547:
546:
541:
536:
535:
531:
509:
508:
504:
491:
488:
483:
475:
471:
459:
369:, known for the
359:Miroslav Katětov
341:Bessel functions
315:Romance language
312:
304:Jan Urban Jarník
272:graph algorithms
235:
230:
200:Miroslav Katětov
172:Doctoral advisor
86:
61:22 December 1897
60:
58:
46:
32:
21:
1941:
1940:
1936:
1935:
1934:
1932:
1931:
1930:
1891:
1890:
1875:
1861:
1855:
1836:
1833:
1831:Further reading
1828:
1827:
1818:
1816:
1809:
1808:
1804:
1797:
1778:
1777:
1770:
1762:
1758:
1748:
1746:
1741:
1740:
1736:
1726:
1724:
1720:
1719:
1715:
1707:
1689:
1688:
1684:
1677:
1660:
1659:
1655:
1648:
1627:
1626:
1617:
1581:
1580:
1576:
1569:
1548:
1547:
1538:
1531:
1516:
1515:
1511:
1504:
1489:
1488:
1484:
1477:
1462:
1461:
1457:
1410:Korte, Bernhard
1408:
1407:
1396:
1384:
1380:
1368:
1364:
1341:
1340:
1329:
1322:
1303:
1302:
1287:
1279:
1275:
1250:
1245:
1244:
1223:
1218:
1162:
1156:
1152:
1107:
1085:
1058:
1033:
990:
955:
949:
884:
855:
787:
754:closed interval
734:Bernard Bolzano
726:
710:
699:
673:
643:
639:
634:
633:
620:
616:
578:
555:
554:
519:
492:
476:
465:
464:
457:
442:integer lattice
426:
390:
306:
300:
228:
214:
139:
97:
88:
84:
75:
73:Austria-Hungary
62:
56:
54:
37:
28:
23:
22:
15:
12:
11:
5:
1939:
1937:
1929:
1928:
1923:
1918:
1913:
1908:
1903:
1893:
1892:
1889:
1888:
1885:Vojtěch Jarník
1874:
1873:External links
1871:
1870:
1869:
1859:
1853:
1832:
1829:
1826:
1825:
1812:Vojtěch Jarník
1802:
1795:
1768:
1756:
1742:Miller, Jeff.
1734:
1713:
1705:
1682:
1675:
1653:
1646:
1615:
1574:
1567:
1536:
1529:
1509:
1502:
1482:
1475:
1455:
1394:
1386:Vojtěch Jarník
1378:
1362:
1327:
1320:
1285:
1283:, p. 168.
1281:Durnová (2004)
1273:
1261:(2): 219–221.
1220:
1219:
1217:
1214:
1198:
1197:
1173:(8): 223–235,
1150:
1105:
1083:
1056:
1031:
1005:(1): 500–518,
988:
948:
945:
923:Joseph Petzval
915:postage stamps
913:. A series of
883:
880:
842:Robert C. Prim
838:weighted graph
830:Otakar Borůvka
786:
783:
756:does not have
742:differentiable
725:
722:
705:, and proved (
696:
695:
680:
676:
672:
667:
663:
657:
654:
649:
646:
642:
575:Big O notation
562:
551:
550:
539:
534:
530:
526:
522:
518:
515:
512:
507:
503:
499:
495:
487:
482:
479:
474:
425:
422:
389:
386:
375:Bohuslav Diviš
299:
296:
276:lattice points
225:Vojtěch Jarník
220:
219:
216:
215:
213:
212:
207:
202:
196:
194:
190:
189:
184:
180:
179:
174:
168:
167:
162:
158:
157:
152:
148:
147:
141:
140:
138:
137:
132:
127:
121:
115:
113:
112:Known for
109:
108:
106:Czechoslovakia
103:
99:
98:
95:Czechoslovakia
89:
87:(aged 72)
81:
77:
76:
63:
52:
48:
47:
39:
38:
36:Vojtěch Jarník
35:
26:
24:
18:Vojtech Jarnik
14:
13:
10:
9:
6:
4:
3:
2:
1938:
1927:
1924:
1922:
1919:
1917:
1914:
1912:
1909:
1907:
1904:
1902:
1899:
1898:
1896:
1886:
1881:
1877:
1876:
1872:
1866:
1865:
1860:
1856:
1854:80-7196-156-6
1850:
1846:
1842:
1841:
1835:
1834:
1830:
1814:
1813:
1806:
1803:
1798:
1796:80-7196-156-6
1792:
1788:
1784:
1783:
1775:
1773:
1769:
1766:, mff.cuni.cz
1765:
1760:
1757:
1745:
1738:
1735:
1723:
1717:
1714:
1708:
1706:9780132762564
1702:
1698:
1697:
1692:
1686:
1683:
1678:
1676:9788072850464
1672:
1668:
1664:
1657:
1654:
1649:
1647:80-7196-156-6
1643:
1639:
1635:
1631:
1624:
1622:
1620:
1616:
1611:
1607:
1603:
1599:
1594:
1589:
1585:
1578:
1575:
1570:
1568:80-7196-156-6
1564:
1560:
1556:
1552:
1545:
1543:
1541:
1537:
1532:
1530:9780824796969
1526:
1522:
1521:
1513:
1510:
1505:
1503:9780191590320
1499:
1495:
1494:
1486:
1483:
1478:
1476:9781447140962
1472:
1468:
1467:
1459:
1456:
1451:
1447:
1442:
1437:
1433:
1429:
1426:(1–3): 1–17.
1425:
1421:
1420:
1415:
1411:
1405:
1403:
1401:
1399:
1395:
1391:
1387:
1382:
1379:
1375:
1374:Veselý (1999)
1371:
1370:Netuka (1998)
1366:
1363:
1359:
1355:
1354:
1349:
1345:
1338:
1336:
1334:
1332:
1328:
1323:
1321:80-7196-156-6
1317:
1313:
1309:
1308:
1300:
1298:
1296:
1294:
1292:
1290:
1286:
1282:
1277:
1274:
1268:
1264:
1260:
1256:
1249:
1242:
1240:
1238:
1236:
1234:
1232:
1230:
1228:
1226:
1222:
1215:
1213:
1211:
1207:
1203:
1195:
1190:
1186:
1181:
1176:
1172:
1168:
1160:
1151:
1147:
1143:
1138:
1133:
1128:
1123:
1119:
1116:(in German),
1115:
1111:
1106:
1103:
1097:
1093:
1089:
1084:
1080:
1076:
1072:
1069:(in German),
1068:
1067:
1062:
1057:
1053:
1049:
1045:
1042:(in German),
1041:
1037:
1032:
1028:
1024:
1020:
1016:
1012:
1008:
1004:
1001:(in German),
1000:
999:
994:
989:
985:
981:
976:
971:
967:
963:
959:
954:
953:
952:
946:
944:
942:
938:
933:
930:
928:
924:
920:
916:
912:
908:
904:
895:
891:
889:
881:
879:
877:
873:
869:
865:
859:
854:
853:Miloš Kössler
849:
847:
843:
839:
835:
831:
827:
823:
819:
815:
811:
807:
800:
796:
793:Animation of
791:
784:
782:
779:
775:
771:
767:
766:Stefan Banach
763:
759:
755:
751:
747:
743:
739:
735:
731:
730:real analysis
723:
721:
719:
714:
708:
702:
678:
674:
670:
665:
661:
655:
652:
647:
644:
640:
632:
631:
630:
627:
623:
614:
610:
606:
603:. He proved (
602:
598:
594:
589:
587:
582:
576:
560:
532:
528:
524:
520:
513:
510:
505:
501:
497:
493:
485:
480:
477:
472:
463:
462:
461:
455:
451:
447:
443:
439:
430:
424:Number theory
423:
421:
419:
415:
411:
410:lattice point
407:
403:
399:
398:number theory
395:
388:Contributions
387:
385:
382:
380:
376:
372:
368:
364:
360:
355:
353:
349:
348:Edmund Landau
344:
342:
338:
337:Mathias Lerch
334:
330:
325:
323:
319:
316:
310:
305:
297:
295:
293:
289:
285:
281:
280:convex curves
277:
273:
269:
265:
264:number theory
260:
258:
254:
250:
246:
242:
241:mathematician
239:
234:
226:
217:
211:
208:
206:
203:
201:
198:
197:
195:
191:
188:
187:Edmund Landau
185:
181:
178:
175:
173:
169:
166:
163:
159:
156:
153:
149:
146:
142:
136:
133:
131:
128:
125:
124:Lattice point
122:
120:
117:
116:
114:
110:
107:
104:
100:
96:
92:
82:
78:
74:
70:
66:
53:
49:
45:
40:
33:
30:
19:
1863:
1839:
1817:, retrieved
1811:
1805:
1781:
1759:
1747:. Retrieved
1737:
1725:. Retrieved
1716:
1695:
1685:
1666:
1656:
1633:
1583:
1577:
1554:
1519:
1512:
1492:
1485:
1465:
1458:
1423:
1417:
1381:
1365:
1351:
1306:
1276:
1258:
1254:
1199:
1170:
1169:(in Czech),
1166:
1159:daných bodů"
1117:
1113:
1095:
1094:(in Czech),
1091:
1070:
1064:
1043:
1039:
1002:
996:
965:
964:(in Czech),
961:
950:
936:
934:
931:
909:district of
900:
885:
850:
803:
778:residual set
727:
712:
700:
697:
625:
621:
597:real numbers
590:
583:
552:
456:with length
454:convex curve
435:
391:
383:
363:chess master
356:
352:habilitation
345:
326:
301:
261:
224:
223:
161:Institutions
144:
85:(1970-09-22)
29:
1906:1970 deaths
1901:1897 births
1727:16 February
1073:: 371–382,
856: [
718:Besicovitch
379:Tibor Šalát
307: [
210:Tibor Šalát
155:Mathematics
102:Nationality
1895:Categories
1843:, Prague:
1819:2017-02-17
1785:, Prague:
1749:2017-02-17
1696:Algorithms
1636:, Prague:
1593:1601.01948
1557:, Prague:
1310:, Prague:
1216:References
1189:0009.13106
1146:0007.40102
1079:55.0719.01
1052:55.0718.01
984:50.0189.02
968:: 98–101,
329:Karel Petr
177:Karel Petr
57:1897-12-22
1610:119304793
1120:: 48–58,
1027:117747514
814:algorithm
648:−
605:1928–1929
481:π
318:philology
820:that he
126:problems
1450:1829832
1388:at the
1098:: 57–63
1019:1544776
903:Ostrava
629:, with
611:) have
69:Bohemia
1851:
1793:
1703:
1673:
1644:
1608:
1565:
1527:
1500:
1473:
1448:
1318:
1208:, and
1187:
1144:
1077:
1050:
1025:
1017:
982:
911:Prague
907:Chodov
703:> 2
446:circle
270:, and
151:Fields
91:Prague
65:Prague
1606:S2CID
1588:arXiv
1251:(PDF)
1023:S2CID
876:Gauss
860:]
772:that
752:of a
311:]
238:Czech
1849:ISBN
1791:ISBN
1729:2017
1701:ISBN
1671:ISBN
1642:ISBN
1563:ISBN
1525:ISBN
1498:ISBN
1471:ISBN
1372:and
1316:ISBN
925:and
864:1934
844:and
808:and
797:for
768:and
707:1929
666:<
450:1926
436:The
361:, a
255:for
80:Died
51:Born
1598:doi
1436:hdl
1428:doi
1424:235
1263:doi
1259:123
1185:Zbl
1175:doi
1142:Zbl
1132:hdl
1122:doi
1075:JFM
1048:JFM
1007:doi
980:JFM
970:doi
804:In
599:by
320:at
278:on
1897::
1847:,
1771:^
1618:^
1604:,
1596:,
1539:^
1446:MR
1444:.
1434:.
1422:.
1412:;
1397:^
1356:,
1350:,
1346:,
1330:^
1288:^
1257:.
1224:^
1204:,
1183:,
1171:63
1140:,
1130:,
1118:21
1071:36
1044:36
1021:,
1015:MR
1013:,
1003:24
978:,
966:53
929:.
858:cs
832:.
711:2/
420:.
408:,
381:.
309:cs
294:.
266:,
259:.
93:,
71:,
67:,
1858:.
1823:.
1800:.
1754:.
1752:.
1731:.
1711:.
1709:.
1651:.
1600::
1590::
1572:.
1534:.
1507:.
1480:.
1452:.
1438::
1430::
1392:,
1325:.
1271:.
1269:.
1265::
1196:.
1177::
1163:n
1157:n
1134::
1124::
1096:6
1009::
972::
862:(
713:k
701:k
679:k
675:q
671:1
662:|
656:q
653:p
645:x
641:|
626:q
624:/
622:p
617:x
579:L
561:O
538:)
533:3
529:/
525:1
521:L
517:(
514:O
511:+
506:3
502:/
498:2
494:L
486:3
478:2
473:3
458:L
227:(
59:)
55:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
