Jørgen Mohr (Latinised ''Georg(ius) Mohr''; 1 April 1640 – 26 January 1697) was a

Danish Danish may refer to: * Something of, from, or related to the country of Denmark People * A national or citizen of Denmark, also called a "Dane," see Demographics of Denmark * Culture of Denmark * Danish people or Danes, people with a Danish a ...

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, structure, space, models, and change. History On ...

, known for being the first to prove the

Mohr–Mascheroni theorem In mathematics, the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. It must be understood that by "any geometric construction", we are refer ...

, which states that any geometric construction which can be done with

compass and straightedge In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an ideali ...

can also be done with compasses alone.

Biography

Mohr was born in

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

, the son of a tradesman named David Mohrendal. Beginning in 1662 he traveled to the

Netherlands ) , anthem = ( en, "William of Nassau") , image_map = , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of the Netherlands , established_title = Before independence , established_date = Spanish Netherl ...

, to study mathematics with

Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of ...

.. In 1672 he published his first book, '' Euclides Danicus'', simultaneously in Copenhagen and Amsterdam, in Danish and Dutch respectively. This book, proving the Mohr–Mascheroni theorem 125 years earlier than

Lorenzo Mascheroni Lorenzo Mascheroni (; May 13, 1750 – July 14, 1800) was an Italian mathematician. Biography He was born near Bergamo, Lombardy. At first mainly interested in the humanities (poetry and Greek language), he eventually became professor of mathem ...

, would languish in obscurity until its rediscovery in 1928.. Mohr served in

Franco-Dutch War The Franco-Dutch War, also known as the Dutch War (french: Guerre de Hollande; nl, Hollandse Oorlog), was fought between France and the Dutch Republic, supported by its allies the Holy Roman Empire, Spain, Brandenburg-Prussia and Denmark-Nor ...

in 1672–1673, and was taken prisoner by the French. By 1673, he had published his second book, ''Compendium Euclidis Curiosi''. A third book was later mentioned by Mohr's son; for many years this was believed to be the ''Gegenübung auf Compendium Euclidis Curiosi'' but argue that it must be a different book, and that the ''Gegenübung'' has a different author.. As well as his work on geometry, Mohr contributed to the theory of

nested radical In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include :\sqrt, which arises in discussing the regular pentagon, and more co ...

s, with the aim of simplifying

Cardano's formula In algebra, a cubic equation in one variable is an equation of the form :ax^3+bx^2+cx+d=0 in which is nonzero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the ...

for the roots of a

cubic polynomial In mathematics, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d where the coefficients , , , and are complex numbers, and the variable takes real values, and a\neq 0. In other words, it is both a polynomial function of degree ...

. While in the Netherlands, Mohr became a friend of

Ehrenfried Walther von Tschirnhaus Ehrenfried Walther von Tschirnhaus (or Tschirnhauß, ; 10 April 1651 – 11 October 1708) was a German mathematician, physicist, physician, and philosopher. He introduced the Tschirnhaus transformation and is considered by some to have been the ...

. The two visited

Gottfried Wilhelm Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...

in France and John Collins in England together. Mohr returned to Denmark in 1681; he had dedicated ''Euclides Danicus'' to

Christian V Christian V (15 April 1646 25 August 1699) was king of Denmark and Norway from 1670 until his death in 1699. Well-regarded by the common people, he was the first king anointed at Frederiksborg Castle chapel as absolute monarch since the decree ...

and hoped for a position in exchange, but was offered only a position as a shipyard supervisor, which he declined. He married Elizabeth von der Linde of Copenhagen on 19 July 1687, and soon after returned to Holland; their son, Peter Georg Mohrenthal, eventually settled in

Dresden Dresden (, ; Upper Saxon: ''Dräsdn''; wen, label=Upper Sorbian, Drježdźany) is the capital city of the German state of Saxony and its second most populous city, after Leipzig. It is the 12th most populous city of Germany, the fourth larg ...

as a bookseller and publisher. In 1695 he took a job with Tschirnhaus, and spent his last few years as a guest in Tschirnhaus's house. He died in Kieslingswalde near

Görlitz Görlitz (; pl, Zgorzelec, hsb, Zhorjelc, cz, Zhořelec, :de:Ostlausitzer Mundart, East Lusatian dialect: ''Gerlz'', ''Gerltz'', ''Gerltsch'') is a town in the Germany, German state of Saxony. It is located on the Lusatian Neisse River, and ...

, Germany. The Georg Mohr competition, which is used to select Danish participants to the

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except i ...

, is named after Mohr.Official website for th
Georg Mohr-Competition
(in Danish), retrieved 27 June 2014.

Biography

References

Further reading