Thomas Clausen (16 January 1801, Snogbæk, Sottrup Municipality,

Duchy of Schleswig The Duchy of Schleswig (; ; ; ; ; ) was a duchy in Southern Jutland () covering the area between about 60 km (35 miles) north and 70 km (45 mi) south of the current border between Germany and Denmark. The territory has been div ...

– 23 May 1885,

Tartu Tartu is the second largest city in Estonia after Tallinn. Tartu has a population of 97,759 (as of 2024). It is southeast of Tallinn and 245 kilometres (152 miles) northeast of Riga, Latvia. Tartu lies on the Emajõgi river, which connects the ...

Imperial Russia Imperial is that which relates to an empire, emperor/empress, or imperialism. Imperial or The Imperial may also refer to: Places United States * Imperial, California * Imperial, Missouri * Imperial, Nebraska * Imperial, Pennsylvania * ...

) was a Danish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

Life

Clausen learned mathematics at home. In 1820, he became a trainee at the

Munich Munich is the capital and most populous city of Bavaria, Germany. As of 30 November 2024, its population was 1,604,384, making it the third-largest city in Germany after Berlin and Hamburg. Munich is the largest city in Germany that is no ...

Optical Institute and in 1824, at the Altona Observatory after he showed Heinrich Christian Schumacher his paper on calculating longitude by the

occultation An occultation is an event that occurs when one object is hidden from the observer by another object that passes between them. The term is often used in astronomy, but can also refer to any situation in which an object in the foreground blocks f ...

of stars by the moon. In 1828, he discovered Clausen's formula. He eventually returned to Munich, where he conceived and published his best known works on mathematics. In 1832, he discovered the Clausen function. In 1842, Clausen was hired by the staff of the

Tartu Observatory The Tartu Observatory () is the largest astronomy, astronomical observatory in Estonia. On 1 January 2018, Tartu Observatory was joined again to the University of Tartu, and the observatory is now an institute of the university. It is located o ...

, becoming its director in 1866–1872. Works by Clausen include studies on the stability of

Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...

comet A comet is an icy, small Solar System body that warms and begins to release gases when passing close to the Sun, a process called outgassing. This produces an extended, gravitationally unbound atmosphere or Coma (cometary), coma surrounding ...

movement, ABC

telegraph code A telegraph code is one of the character encodings used to transmit information by telegraphy. Morse code is the best-known such code. ''Telegraphy'' usually refers to the electrical telegraph, but telegraph systems using the optical telegraph w ...

and calculation of 250 decimals of pi (later, only 248 were confirmed to be correct). In 1840, he discovered the Von Staudt–Clausen theorem. Also in 1840, he also found two compass and straightedge constructions of

lune Lune may refer to: Rivers *River Lune, in Lancashire and Cumbria, England *River Lune, Durham, in County Durham, England *Lune (Weser), a 43 km-long tributary of the Weser in Germany *Lune River (Tasmania), in south-eastern Tasmania, Australia Pl ...

s with equal area to a square, adding to three (including the

lune of Hippocrates In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle. Equivalently, it is a non-convex pl ...

) known to the ancient Greek mathematician

Hippocrates of Chios Hippocrates of Chios (; c. 470 – c. 421 BC) was an ancient Greek mathematician, geometer, and astronomer. He was born on the isle of Chios, where he was originally a merchant. After some misadventures (he was robbed by either pirates or ...

; it was later shown that these five lunes are the only possible solutions to this problem.. Translated from Postnikov's 1963 Russian book on

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems ...

. In 1854, he factored the sixth

Fermat number In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a natural number, positive integer of the form:F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers ...

as 2⁶⁴+1 = 67280421310721 × 274177.

Notes

References

* * * {{DEFAULTSORT:Clausen, Thomas 1801 births 1885 deaths 19th-century Danish mathematicians 19th-century Danish astronomers People from the Duchy of Schleswig People from the Kingdom of Bavaria Expatriates in the Russian Empire