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

, known for being the first to prove the Mohr–Mascheroni theorem, 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 Idealiz ...

can also be done with compasses alone.

Biography

Mohr was born in

Copenhagen Copenhagen ( ) is the capital and most populous city of Denmark, with a population of 1.4 million in the Urban area of Copenhagen, urban area. The city is situated on the islands of Zealand and Amager, separated from Malmö, Sweden, by the ...

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

Netherlands , Terminology of the Low Countries, informally Holland, is a country in Northwestern Europe, with Caribbean Netherlands, overseas territories in the Caribbean. It is the largest of the four constituent countries of the Kingdom of the Nether ...

, to study mathematics with

Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...

.. In 1672 he published his first book, ''

Euclides Danicus ''Euclides Danicus'' (the Danish Euclid) is one of three books of mathematics written by Georg Mohr. It was published in 1672 simultaneously in Copenhagen and Amsterdam, in Danish and Dutch respectively. It contains the first proof of the Mohr� ...

'', 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 geometer and mathematician. Biography He was born near Bergamo, Lombardy. At first mainly interested in the humanities (poetry and Greek language), he eventually became profe ...

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

Franco-Dutch War The Franco-Dutch War, 1672 to 1678, was primarily fought by Kingdom of France, France and the Dutch Republic, with both sides backed at different times by a variety of allies. Related conflicts include the 1672 to 1674 Third Anglo-Dutch War and ...

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 pentagon, regular pentagon, an ...

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 not zero. The solutions of this equation are called root of a function, roots of the cubic function defined by the left-hand side of the equ ...

for the roots of a

cubic polynomial In mathematics, a cubic function is a function (mathematics), function of the form f(x)=ax^3+bx^2+cx+d, that is, a polynomial function of degree three. In many texts, the ''coefficients'' , , , and are supposed to be real numbers, and the func ...

. 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 Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to ...

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 de ...

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 German, Upper Saxon: ''Dräsdn''; , ) is the capital city of the States of Germany, German state of Saxony and its second most populous city after Leipzig. It is the List of cities in Germany by population, 12th most p ...

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 (; ; ; ; ; Lusatian dialects, East Lusatian: , , ) is a town in the Germany, German state of Saxony. It is on the river Lusatian Neisse and is the largest town in Upper Lusatia, the second-largest town in the region of Lusatia after ...

, 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. It is widely regarded as the most prestigious mathematical competition in the wor ...

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

Biography

References

Further reading