Carl Størmer | |
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| Born | Fredrik Carl Mülertz Størmer (1874-09-03)3 September 1874 |
| Died | 13 August 1957(1957-08-13) (aged 82) |
| Nationality | Norwegian |
| Alma mater | University of Oslo |
| Known for | number theory aurorae |
| Awards | |
| Scientific career | |
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Fredrik Carl Mülertz Størmer (Norwegian pronunciation:[fʁɛdʁɪkkaːlˈmʏlɐːt͡s̍ˈʃtøːmɐː]) (3 September 1874 – 13 August 1957) was aNorwegianmathematician andastrophysicist. In mathematics, he is known for his work innumber theory, including the calculation ofπ andStørmer's theorem on consecutive smooth numbers. In physics, he is known for studying the movement of charged particles in themagnetosphere and the formation ofaurorae, and for his book on these subjects,From the Depths of Space to the Heart of the Atom. He worked for many years as a professor of mathematics at theUniversity of Oslo in Norway. Acrater on the far side of the Moon is named after him.
Størmer was born on 3 September 1874 inSkien, the only child of a pharmacist Georg Ludvig Størmer (1842–1930) and Elisabeth Amalie Johanne Henriette Mülertz (1844–1916).[1][2] His uncle was the entrepreneur and inventorHenrik Christian Fredrik Størmer.[1][2]
Størmer studied mathematics at theRoyal Frederick University in Kristiania, Norway (now the University of Oslo, in Oslo) from 1892 to 1897, earning the rank ofcandidatus realium in 1898. He then studied withPicard,Poincaré,Painlevé,Jordan,Darboux, andGoursat at theSorbonne inParis from 1898 to 1900. He returned to Kristiania in 1900 as aresearch fellow in mathematics, visited theUniversity of Göttingen 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 elected as the first president of the newly formedNorwegian Mathematical Society. He participated regularly in Scandinavian mathematical congresses, and was president of the 1936International Congress of Mathematicians 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, atBlindern.[1][3][4][5]
He was also an amateurstreet photographer,[6] beginning in his student days. In the years 1893-1897, he documented daily life on the streets of Oslo using a miniature CP Stirn spy camera. Between 1942 and 1943, he shared a small portion of his works with the public. However, it was not until he was 70 years old that he organized an exhibition showcasing all his historical photographs of celebrities that he had taken over the years.[7] For instance it included one ofHenrik Ibsen strolling downKarl Johans gate, the main road in Oslo.[1] Most of these can now be viewed in Norway's Digitalt Museum.[8]
He was also a supervisory council member of the insurance companyForsikringsselskapet Norden.[9]
In February 1900 he married consul's daughter Ada Clauson (1877–1973), with whom he eventually had five children.[4] Their sonLeif Størmer became a professor ofhistorical geology at theUniversity of Oslo.[2] His daughter Henny married landownerCarl Otto Løvenskiold.[10] Carl Størmer is also the grandfather of the mathematicianErling Størmer.[11][12]
Størmer's first mathematical publication, published when he was a beginning student at the age of 18, concernedtrigonometricseries generalizing theTaylor expansion of thearcsine function. He revisited this problem a few years later. Next, he systematically investigatedMachin-like formula by which the numberπ may be represented as a rational combination of the so-called "Gregory numbers" of the formarctan 1/n.Machin's original formula,
is of this type, and Størmer showed that there were three other ways of representingπ 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.[3] These representations led to fast algorithms for computingnumerical approximations ofπ. In particular, a four-term representation found by Størmer,
was used in a record-setting calculation ofπ to 1,241,100,000,000 decimal digits in 2002 byYasumasa Kanada.[13] Størmer is also noted for theStørmer numbers, which arose from the decomposition of Gregory numbers in Størmer's work.[14]
Størmer's theorem, which he proved in 1897, shows that, for any finite setP ofprime numbers, there are only finitely many pairs of consecutiveintegers having only the numbers fromP as theirprime factors. In addition, Størmer describes analgorithm for finding all such pairs. Thesuperparticular ratios generated by these consecutive pairs are of particular importance in music theory.[15] Størmer proves this theorem by reducing the problem to a finite set ofPell equations, and the theorem itself can also be interpreted as describing the possible factorizations of solutions to Pell's equation. Chapman quotesLouis Mordell as saying "His result is very pretty, and there are many applications of it."[1]
Additional subjects of Størmer's mathematical research includedLie groups, thegamma function, andDiophantine approximation ofalgebraic numbers and of thetranscendental numbers arising fromelliptic functions. From 1905 Størmer was an editor of the journalActa Mathematica, and he was also an editor of the posthumously-published mathematical works ofNiels Henrik Abel andSophus Lie.[1][3]
From 1903, when Størmer first observedKristian Birkeland's experimental attempts to explain theaurora borealis, 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 amagnetizedsphere, and Størmer eventually published over 48 papers on the motion of charged particles.[16] By modeling the problem usingdifferential equations andpolar coordinates, Størmer was able to show that theradius of curvature 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 usedVerlet integration, which is therefore also known asStörmer's method.[3]Ernst Brüche andWillard Harrison Bennett verified experimentally Størmer's predicted particle motions; Bennett called his experimental apparatus "Störmertron" in honor of Størmer.[1] 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 magnetic field, explaining the convoluted shapes of aurorae.[17] 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 magnetosphericring current[1] andVan Allen radiation belts.[18]
As well as modeling these phenomena mathematically, Størmer took manyphotographs of aurorae, from 20 different observatories across Norway. He measured their heights and latitudes bytriangulation 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 aurorae can be as high as 1000 km above ground.[19][20]
Størmer's book,From the Depths of Space to the Heart of the Atom, describing his work in this area, was translated into five different languages from the original Norwegian.[3] A second book,The Polar Aurora (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.[21] Heard writes, "The Polar Aurora 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."[21]
Other astrophysical phenomena investigated by Størmer include pulsations of theearth's magnetic field,echoing inradio transmissions,nacreous clouds andnoctilucent clouds,zodiacal light,meteor trails, thesolar corona and solar vortices, andcosmic rays.[1]
Størmer was aForeign Member of the Royal Society (ForMemRS)[1] and a Corresponding Member of theFrench Academy of Sciences.[1] He was also a member of theNorwegian Academy of Science and Letters from 1900.[2] He was givenhonorary degrees byOxford University (in 1947), theUniversity of Copenhagen (1951), and theSorbonne (1953), and in 1922 the French Academy awarded him theirJanssen Medal.[1][4][2] Three times Størmer was aplenary speaker in the International Congress of Mathematicians (1908 in Rome, 1924 in Toronto, and 1936 in Oslo);[22] he was an invited speaker of the ICM in 1920 in Strasbourg[23] and in 1932 in Zurich.[22] In 1971, the craterStörmer on the far side of the Moon was named after him.[24] The Lie-Størmer Center atUiT - The Arctic University of Norway is named after him
In 1902, Størmer was decorated withKing Oscar II's Medal of Merit in gold. He was also decorated as a Knight, First Order of theOrder of St. Olav in 1939. He was upgraded toGrand Cross of the Order of St. Olav in 1954.[2]
