Carl Størmer

Mathematical research Størmer's first mathematical publication, published when he was a beginning student at the age of 18, concerned trigonometric series generalizing the Taylor expansion of the arcsine function. He revisited this problem a few years later. Next, he systematically investigated Machin-like formula by which the number may be represented as a rational combination of the so-called "Gregory numbers" of the form . Machin's original formula,

is of this type, and Størmer showed that there were three other ways of representing 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. Størmer is also noted for the Størmer numbers, which arose from the decomposition of Gregory numbers in Størmer's work.

Størmer's theorem, which he proved in 1897, shows that, for any finite set of prime numbers, there are only finitely many pairs of consecutive integers having only the numbers from as their prime factors. In addition, Størmer describes an algorithm for finding all such pairs. The superparticular ratios 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 Pell equations, and the theorem itself can also be interpreted as describing the possible factorizations of solutions to Pell's equation. Chapman quotes Louis Mordell as saying "His result is very pretty, and there are many applications of it." By modeling the problem using differential equations and polar coordinates, Størmer was able to show that the radius 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 used Verlet integration, which is therefore also known as Störmer's method. 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 ring current

As well as modeling these phenomena mathematically, Størmer took many photographs of aurorae, from 20 different observatories across Norway. He measured their heights and latitudes by triangulation 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.

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.

Other astrophysical phenomena investigated by Størmer include pulsations of the earth's magnetic field, echoing in radio transmissions, nacreous clouds and noctilucent clouds, zodiacal light, meteor trails, the solar corona and solar vortices, and cosmic rays. and in 1932 in Zurich. In 1971, the crater Störmer on the far side of the Moon was named after him. The Lie-Størmer Center at UiT - The Arctic University of Norway is named after him

In 1902, Størmer was decorated with King Oscar II's Medal of Merit in gold. He was also decorated as a Knight, First Order of the Order of St. Olav in 1939. He was upgraded to Grand Cross of the Order of St. Olav in 1954.