254:
40:
735:
805:
from multiple observatories, and showed that the aurora are typically as high as 100 kilometers above ground. He classified them by their shapes, and discovered in 1926 the "solar-illuminated aurora", a phenomenon that can occur at twilight when the upper parts of an aurora are lit by the sun; these
786:
magnetic field, explaining the convoluted shapes of aurorae. Størmer also considered the possibility that particles might be trapped within the geomagnetic field, and worked out the orbits of these trapped particles. Størmer's work on this subject applies to what are today called the magnetospheric
324:
in 1902, and returned to
Kristiania in 1903, where he was appointed as a professor of mathematics, a position he held for 43 years. After he received a permanent position in Kristiania, Størmer published his subsequent writings under a shortened version of his name, Carl Størmer. In 1918, he was
785:
verified experimentally Størmer's predicted particle motions; Bennett called his experimental apparatus "Störmertron" in honor of Størmer. Størmer's calculations showed that small variations in the trajectories of particles approaching the earth would be magnified by the effects of the Earth's
507:
as a rational combination of two
Gregory numbers. He then investigated combinations of three Gregory numbers, and found 102 representations of π of this form, but was unable to determine whether there might be additional solutions of this type. These representations led to fast algorithms for
626:
817:(Oxford Press, 1955), contains both his experimental work on aurorae and his mathematical attempts to model them. In his review of this book, Canadian astronomer John F. Heard calls Størmer "the acknowledged authority" on aurorae. Heard writes, "
498:
521:
897:
333:
in Oslo (from 1924 the new name of
Kristiania). Størmer was also affiliated with the Institute of Theoretical Astrophysics at the University of Oslo, which was founded in 1934. He died on 13 August 1957, at
750:, he was fascinated by aurorae and related phenomena. His first work on the subject attempted to model mathematically the paths taken by charged particles perturbed by the influence of a
345:, beginning in his student days. Near the age of 70 he put on an exhibition in Oslo of the photographs of celebrities that he had taken over the years. For instance it included one of
253:
2047:
269:, the only child of a pharmacist Georg Ludvig Størmer (1842–1930) and Elisabeth Amalie Johanne Henriette Mülertz (1844–1916). His uncle was the entrepreneur and inventor
2062:
769:
of any particle's path is proportional to the square of its distance from the sphere's center. To solve the resulting differential equations numerically, he used
1788:
965:
677:
generated by these consecutive pairs are of particular importance in music theory. Størmer proves this theorem by reducing the problem to a finite set of
900:(1908 in Rome, 1924 in Toronto, and 1936 in Oslo); he was an invited speaker of the ICM in 1920 in Strasbourg and in 1932 in Zurich. In 1971, the crater
434:
2057:
2017:
821:
will undoubtedly remain for many years a standard reference book; it belongs on the desk of anyone whose work or interest is involved with aurorae."
1659:
2052:
621:{\displaystyle \textstyle \pi =176\arctan {\frac {1}{57}}+28\arctan {\frac {1}{239}}-48\arctan {\frac {1}{682}}+96\arctan {\frac {1}{12943}}}
1633:
681:, and the theorem itself can also be interpreted as describing the possible factorizations of solutions to Pell's equation. Chapman quotes
1552:
893:
149:
873:
330:
258:
144:
1578:
373:
1121:
1180:
813:, describing his work in this area, was translated into five different languages from the original Norwegian. A second book,
1311:
1141:
360:
In
February 1900 he married consul's daughter Ada Clauson (1877–1973), with whom he eventually had five children. Their son
2012:
1399:
270:
261:, Zürich 1932; he was accompanied by Ms. Størmer (sitting left, dark clothing) and Ms. Lövenskiold (sitting, white hat).
2007:
1771:
2042:
2027:
1360:
766:
757:, and Størmer eventually published over 48 papers on the motion of charged particles. By modeling the problem using
1938:
1461:
388:
Størmer's first mathematical publication, published when he was a beginning student at the age of 18, concerned
2022:
1969:
326:
2032:
1390:
225:
on consecutive smooth numbers. In physics, he is known for studying the movement of charged particles in the
1780:
354:
2002:
1807:
869:
1674:
801:
of aurorae, from 20 different observatories across Norway. He measured their heights and latitudes by
321:
2037:
1671:
Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920
1036:
825:
697:
1710:; Bell, B. (1971). "Report on Lunar Nomenclature by The Working Group of Commission 17 of the IAU".
1892:
1126:
885:
791:
782:
329:. He participated regularly in Scandinavian mathematical congresses, and was president of the 1936
280:
in
Kristiania, Norway (now the University of Oslo, in Oslo) from 1892 to 1897, earning the rank of
20:
1116:
1637:
646:
285:
222:
1902:
1877:
1764:
1749:
1556:
1027:
509:
1912:
1882:
1344:
1285:
1256:
758:
705:
674:
403:
function. He revisited this problem a few years later. Next, he systematically investigated
1997:
1992:
1954:
1907:
1719:
1699:
1508:
1470:
1423:
1370:
392:
353:, the main road in Oslo. He was also a supervisory council member of the insurance company
39:
8:
1802:
1113:
889:
404:
309:
301:
1827:
1723:
1512:
1474:
901:
242:
1735:
1586:
1534:
1411:
1328:
1145:
990:
982:
770:
747:
743:
734:
678:
369:
365:
342:
277:
238:
230:
125:
111:
305:
1847:
1757:
1739:
1538:
1452:
1356:
1198:
1176:
1041:
912:
881:
829:
719:
709:
503:
is of this type, and Størmer showed that there were three other ways of representing
154:
90:
1529:
1337:
994:
640:
377:
289:
1922:
1872:
1867:
1842:
1812:
1727:
1524:
1516:
1478:
1403:
1348:
1251:
1087:
1023:
974:
762:
714:
701:
493:{\displaystyle \textstyle \pi =16\arctan {\frac {1}{5}}-4\arctan {\frac {1}{239}},}
396:
350:
293:
1897:
1707:
1703:
1419:
1366:
1315:
1308:
1214:
1149:
911:'s Medal of Merit in gold. He was also decorated as a Knight, First Order of the
877:
636:
317:
824:
Other astrophysical phenomena investigated by Størmer include pulsations of the
778:
718:, and he was also an editor of the posthumously-published mathematical works of
361:
1837:
1496:
1332:
1219:
841:
837:
693:
414:
297:
1352:
685:
as saying "His result is very pretty, and there are many applications of it."
1986:
1887:
1862:
1784:
908:
865:
802:
682:
654:
226:
212:
204:
139:
121:
68:
1482:
1959:
1385:
978:
849:
787:
666:
643:, which arose from the decomposition of Gregory numbers in Størmer's work.
389:
346:
208:
182:
1852:
1832:
1822:
1817:
1917:
916:
425:
177:
1662:
Méthode d'integration numérique des équations différentielles ordinaires
1307:
Associated press, 6 December 2002; letter from Kanada, 20 October 2005,
1857:
1731:
1520:
1415:
1092:
1075:
1071:
1031:
853:
798:
723:
281:
986:
797:
As well as modeling these phenomena mathematically, Størmer took many
1224:
689:
670:
1456:
1407:
1247:
658:
335:
1280:
400:
19:"Størmer" redirects here. For other people with the surname, see
1779:
688:
Additional subjects of Størmer's mathematical research included
237:. He worked for many years as a professor of mathematics at the
898:
845:
754:
751:
413:
may be represented as a rational combination of the so-called "
201:
101:
1196:"Forsikringsaktieselskapet Nordens overskudd 377,000 kroner".
1173:
80 millioner bilder: Norsk kulturhistorisk fotografi 1855–2005
963:
Chapman, S. (1958). "Fredrik Carl Mülertz Störmer 1874-1957".
515:. In particular, a four-term representation found by Størmer,
833:
313:
266:
64:
376:. Carl Størmer is also the grandfather of the mathematician
1582:
1499:(1962). "Energetic particles in the inner Van Allen belt".
86:
1698:
649:, which he proved in 1897, shows that, for any finite set
316:
from 1898 to 1900. He returned to
Kristiania in 1900 as a
892:(1953), and in 1922 the French Academy awarded him their
2048:
Members of the
Norwegian Academy of Science and Letters
1441:. Springer, Dordrecht, The Netherlands. pp. 1–195.
1388:(1972). "More on the superparticular ratios in music".
1175:(in Norwegian). Oslo: Forlaget Press. pp. 142–45.
408:
216:
525:
438:
806:
aurorae can be as high as 1000 km above ground.
524:
437:
1171:
Ekeberg, Jonas; Lund, Harald Østgaard, eds. (2008).
966:
Biographical
Memoirs of Fellows of the Royal Society
657:, there are only finitely many pairs of consecutive
1613:
325:elected as the first president of the newly formed
1336:
620:
492:
1611:Heard, J. F. "The Polar Aurora by Carl Størmer".
1462:Terrestrial Magnetism and Atmospheric Electricity
1212:
1111:
904:on the far side of the Moon was named after him.
811:From the Depths of Space to the Heart of the Atom
712:. From 1905 Størmer was an editor of the journal
235:From the Depths of Space to the Heart of the Atom
2063:Presidents of the Norwegian Mathematical Society
1984:
245:on the far side of the Moon is named after him.
635:to 1,241,100,000,000 decimal digits in 2002 by
1555:. Northern Lights Center. 2003. Archived from
866:Foreign Member of the Royal Society (ForMemRS)
211:. In mathematics, he is known for his work in
1765:
1457:"Störmer's work on the physics of the aurora"
738:Carl Størmer with assistant Birkeland in 1910
1383:
631:was used in a record-setting calculation of
1170:
248:
1772:
1758:
1107:
1105:
1103:
200:(3 September 1874 – 13 August 1957) was a
38:
2058:Members of the French Academy of Sciences
1628:
1626:
1528:
1327:
1091:
729:
2018:Academic staff of the University of Oslo
1673:. 1921. pp. 243–257. Archived from
1606:
1604:
1436:
874:Norwegian Academy of Science and Letters
746:'s experimental attempts to explain the
733:
383:
331:International Congress of Mathematicians
265:Størmer was born on 3 September 1874 in
259:International Congress of Mathematicians
252:
16:Norwegian geophysicist and mathematician
1451:
1289:(in Norwegian). Oslo: Kunnskapsforlaget
1260:(in Norwegian). Oslo: Kunnskapsforlaget
1122:MacTutor History of Mathematics Archive
1100:
962:
742:From 1903, when Størmer first observed
372:. His daughter Henny married landowner
1985:
1623:
1585:IMAGE Education Center. Archived from
1144:(in Norwegian). Institute of Physics,
1066:
1064:
1062:
1060:
1058:
958:
956:
954:
952:
233:, and for his book on these subjects,
1753:
1601:
1164:
1018:
1016:
1014:
1012:
1010:
1008:
1006:
1004:
950:
948:
946:
944:
942:
940:
938:
936:
934:
932:
257:Carl Størmer (mid of top row) at the
2053:Foreign members of the Royal Society
1495:
1070:
1022:
907:In 1902, Størmer was decorated with
859:
765:, Størmer was able to show that the
669:. In addition, Størmer describes an
1400:Mathematical Association of America
1139:
1055:
773:, which is therefore also known as
276:Størmer studied mathematics at the
13:
1634:"ICM Plenary and Invited speakers"
1133:
1001:
929:
919:of the Order of St. Olav in 1954.
868:and a Corresponding Member of the
14:
2074:
1610:
1343:. New York: Copernicus. pp.
1278:
1245:
1939:Prince Philip, Duke of Edinburgh
1437:Egeland, Alv; Burke, William J.
673:for finding all such pairs. The
639:. Størmer is also noted for the
271:Henrik Christian Fredrik Størmer
1692:
1652:
1571:
1545:
1489:
1445:
1430:
1377:
1321:
1301:
1272:
1213:Steenstrup, Bjørn, ed. (1948).
215:, including the calculation of
1970:Ralph Walter Graystone Wyckoff
1239:
1206:
1189:
1142:"Fredrik Carl Mülertz Størmer"
1117:"Fredrik Carl Mülertz Størmer"
872:. He was also a member of the
327:Norwegian Mathematical Society
284:in 1898. He then studied with
1:
1439:Carl Størmer: Auroral Pioneer
1391:American Mathematical Monthly
1335:(1996). "Størmer's Numbers".
1309:online at super-computing.org
922:
661:having only the numbers from
1898:John Ashworth Ratcliffe
915:in 1939. He was upgraded to
896:. Three times Størmer was a
510:numerical approximations of
320:in mathematics, visited the
198:Fredrik Carl Mülertz Størmer
51:Fredrik Carl Mülertz Størmer
7:
1878:Leonard Bessemer Pfeil
840:and luminous night clouds,
355:Forsikringsselskapet Norden
10:
2079:
2013:University of Paris alumni
1076:"Carl Störmer in memoriam"
870:French Academy of Sciences
278:Royal Frederick University
18:
2008:University of Oslo alumni
1947:
1931:
1795:
1353:10.1007/978-1-4612-4072-3
1279:Godal, Anne Marit (ed.).
1037:Norsk biografisk leksikon
792:Van Allen radiation belts
698:Diophantine approximation
191:
170:
163:
131:
117:
107:
97:
75:
46:
37:
30:
2043:20th-century astronomers
2028:Norwegian mathematicians
1818:Arthur Herbert Cook
1530:2027/uiug.30112106689950
1215:"Løvenskiold, Carl Otto"
1202:. 2 May 1941. p. 5.
1127:University of St Andrews
886:University of Copenhagen
876:from 1900. He was given
852:and solar vortices, and
783:Willard Harrison Bennett
249:Personal life and career
1823:Sydney John Folley
1483:10.1029/TE013i001p00023
341:He was also an amateur
322:University of Göttingen
155:Grand Cross of St. Olav
1903:Thomas Alan Stephenson
1893:William John Pugh
1223:(in Norwegian). Oslo:
1040:(in Norwegian). Oslo:
979:10.1098/rsbm.1958.0021
826:earth's magnetic field
759:differential equations
739:
730:Astrophysical research
706:transcendental numbers
675:superparticular ratios
622:
494:
364:became a professor of
262:
2023:Norwegian astronomers
1913:Petrus Johann du Toit
1883:James Arthur Prescott
1873:Albert Neuberger
1712:Space Science Reviews
1501:Space Science Reviews
1314:12 March 2011 at the
1286:Store norske leksikon
1257:Store norske leksikon
737:
623:
495:
384:Mathematical research
374:Carl Otto Løvenskiold
256:
229:and the formation of
2033:Norwegian physicists
1955:Herbert McLean Evans
1908:William Homan Thorpe
1114:Robertson, Edmund F.
522:
435:
407:by which the number
1803:Carlyle Smith Beals
1724:1971SSRv...12..136M
1640:on 24 November 2017
1513:1962SSRv....1..278H
1475:1908TeMAE..13...23N
1339:The Book of Numbers
1246:Vatne, Jon Eivind.
1112:O'Connor, John J.;
767:radius of curvature
405:Machin-like formula
343:street photographer
1732:10.1007/BF00171763
1680:on 29 October 2017
1559:on 1 December 2008
1521:10.1007/BF00240580
1146:University of Oslo
1093:10.1007/BF02559599
771:Verlet integration
744:Kristian Birkeland
740:
710:elliptic functions
618:
617:
490:
489:
428:original formula,
370:University of Oslo
366:historical geology
282:candidatus realium
263:
239:University of Oslo
112:University of Oslo
2003:People from Skien
1978:
1977:
1848:Joseph Hutchinson
1833:Geoffrey Gee
1664:par Carl Störmer"
1252:Godal, Anne Marit
1199:Aftenposten Aften
1182:978-82-7547-315-6
1042:Kunnskapsforlaget
913:Order of St. Olav
882:Oxford University
860:Awards and honors
763:polar coordinates
720:Niels Henrik Abel
702:algebraic numbers
647:Størmer's theorem
615:
593:
571:
549:
484:
462:
395:generalizing the
223:Størmer's theorem
195:
194:
165:Scientific career
145:Norwegian Academy
91:Kingdom of Norway
2070:
2038:Number theorists
1923:Alfred Ubbelohde
1868:Kurt Mendelssohn
1853:Raymond Ing
1843:Gerhard Herzberg
1828:Herbert Fröhlich
1813:David Catcheside
1774:
1767:
1760:
1751:
1750:
1744:
1743:
1696:
1690:
1689:
1687:
1685:
1679:
1668:
1656:
1650:
1649:
1647:
1645:
1636:. Archived from
1630:
1621:
1620:
1608:
1599:
1598:
1596:
1594:
1575:
1569:
1568:
1566:
1564:
1549:
1543:
1542:
1532:
1493:
1487:
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1443:
1442:
1434:
1428:
1427:
1381:
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1374:
1342:
1325:
1319:
1305:
1299:
1298:
1296:
1294:
1276:
1270:
1269:
1267:
1265:
1248:"Erling Størmer"
1243:
1237:
1236:
1234:
1232:
1210:
1204:
1203:
1193:
1187:
1186:
1168:
1162:
1161:
1159:
1157:
1148:. Archived from
1137:
1131:
1130:
1109:
1098:
1097:
1095:
1080:Acta Mathematica
1068:
1053:
1052:
1050:
1048:
1020:
999:
998:
960:
888:(1951), and the
878:honorary degrees
819:The Polar Aurora
815:The Polar Aurora
809:Størmer's book,
775:Störmer's method
715:Acta Mathematica
664:
652:
634:
627:
625:
624:
619:
616:
608:
594:
586:
572:
564:
550:
542:
513:
506:
499:
497:
496:
491:
485:
477:
463:
455:
423:
411:
397:Taylor expansion
351:Karl Johans gate
219:
82:
61:3 September 1874
60:
58:
42:
28:
27:
2078:
2077:
2073:
2072:
2071:
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1983:
1982:
1979:
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1943:
1927:
1791:
1778:
1748:
1747:
1697:
1693:
1683:
1681:
1677:
1666:
1658:
1657:
1653:
1643:
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1624:
1609:
1602:
1592:
1590:
1577:
1576:
1572:
1562:
1560:
1551:
1550:
1546:
1497:Hess, Wilmot N.
1494:
1490:
1450:
1446:
1435:
1431:
1408:10.2307/2317424
1384:Halsey, G. D.;
1382:
1378:
1363:
1333:Guy, Richard K.
1329:Conway, John H.
1326:
1322:
1316:Wayback Machine
1306:
1302:
1292:
1290:
1277:
1273:
1263:
1261:
1244:
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1211:
1207:
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1155:
1153:
1138:
1134:
1110:
1101:
1069:
1056:
1046:
1044:
1021:
1002:
961:
930:
925:
884:(in 1947), the
862:
838:nacreous clouds
836:transmissions,
748:aurora borealis
732:
662:
650:
641:Størmer numbers
637:Yasumasa Kanada
632:
607:
585:
563:
541:
523:
520:
519:
511:
504:
476:
454:
436:
433:
432:
418:
415:Gregory numbers
409:
386:
349:strolling down
318:research fellow
251:
217:
187:
159:
124:
108:Alma mater
93:
84:
80:
71:
62:
56:
54:
53:
52:
33:
24:
17:
12:
11:
5:
2076:
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2055:
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2025:
2020:
2015:
2010:
2005:
2000:
1995:
1976:
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1972:
1967:
1962:
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1941:
1935:
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1845:
1840:
1838:Hans Heilbronn
1835:
1830:
1825:
1820:
1815:
1810:
1805:
1799:
1797:
1793:
1792:
1777:
1776:
1769:
1762:
1754:
1746:
1745:
1718:(2): 136–186.
1691:
1651:
1622:
1600:
1589:on 12 May 2011
1579:"Carl Stormer"
1570:
1544:
1507:(2): 278–312.
1488:
1453:Nutting, P. G.
1444:
1429:
1376:
1361:
1320:
1300:
1281:"Leif Størmer"
1271:
1238:
1205:
1188:
1181:
1163:
1140:Egeland, Alf.
1132:
1099:
1086:(1–2): I–VII.
1054:
1028:"Carl Størmer"
1000:
927:
926:
924:
921:
864:Størmer was a
861:
858:
842:zodiacal light
731:
728:
694:gamma function
679:Pell equations
629:
628:
614:
611:
606:
603:
600:
597:
592:
589:
584:
581:
578:
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570:
567:
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559:
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548:
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540:
537:
534:
531:
528:
501:
500:
488:
483:
480:
475:
472:
469:
466:
461:
458:
453:
450:
447:
444:
441:
417:" of the form
385:
382:
378:Erling Størmer
250:
247:
209:astrophysicist
193:
192:
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188:
186:
185:
180:
174:
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79:13 August 1957
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1227:. p. 344
1226:
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1220:Hvem er hvem?
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707:
703:
699:
695:
691:
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683:Louis Mordell
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667:prime factors
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241:in Norway. A
240:
236:
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227:magnetosphere
224:
220:
214:
213:number theory
210:
206:
205:mathematician
203:
199:
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150:Janssen Medal
148:
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143:
141:
140:Royal Society
138:Foreign Mem.
137:
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127:
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122:number theory
120:
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69:Sweden-Norway
66:
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1980:
1965:Carl Størmer
1964:
1960:Karl Lashley
1715:
1711:
1704:Minnaert, M.
1694:
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1675:the original
1670:
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1638:the original
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1557:the original
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1500:
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1150:the original
1135:
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1079:
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1035:
1024:Grøn, Øyvind
970:
964:
906:
863:
850:solar corona
848:trails, the
823:
818:
814:
810:
808:
796:
788:ring current
779:Ernst Brüche
774:
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713:
687:
645:
630:
502:
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387:
362:Leif Størmer
359:
347:Henrik Ibsen
340:
275:
264:
234:
197:
196:
183:astrophysics
164:
81:(1957-08-13)
32:Carl Størmer
25:
1998:1957 deaths
1993:1874 births
1918:Alan Turing
1708:Dollfus, A.
1231:25 February
1072:Brun, Viggo
1047:25 December
1032:Helle, Knut
973:: 257–279.
917:Grand Cross
854:cosmic rays
799:photographs
704:and of the
178:mathematics
98:Nationality
1987:Categories
1932:Statute 12
1858:David Lack
1684:28 October
1644:30 January
1619:: 117–118.
1563:1 December
1293:29 October
923:References
752:magnetized
724:Sophus Lie
690:Lie groups
508:computing
57:1874-09-03
1808:John Boyd
1740:122125855
1553:"Størmer"
1539:121197701
1469:(1): 23.
1225:Aschehoug
671:algorithm
665:as their
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102:Norwegian
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1074:(1958).
1026:(2004).
995:74137537
890:Sorbonne
659:integers
426:Machin's
336:Blindern
310:Sorbonne
294:Painlevé
290:Poincaré
1948:Foreign
1796:Fellows
1789:in 1951
1783:of the
1781:Fellows
1720:Bibcode
1509:Bibcode
1471:Bibcode
1424:0313189
1416:2317424
1371:1411676
1345:245–248
1254:(ed.).
1034:(ed.).
902:Störmer
830:echoing
401:arcsine
399:of the
368:at the
308:at the
306:Goursat
302:Darboux
231:aurorae
126:aurorae
21:Stormer
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1537:
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580:arctan
558:arctan
536:arctan
471:arctan
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393:series
304:, and
298:Jordan
286:Picard
243:crater
171:Fields
132:Awards
1736:S2CID
1678:(PDF)
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1535:S2CID
1412:JSTOR
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1156:5 May
1030:. In
991:S2CID
983:JSTOR
834:radio
613:12943
314:Paris
267:Skien
65:Skien
1686:2017
1646:2014
1595:2011
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781:and
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